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LIBRARY OF CONGRESS. 

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UNITED STATES OF AMEBICA. 



TEXT-BOOK 



POPULAR ASTRONOMi 



T 



FOR THE USE OF 



COLLEGES, ACADEMIES, AND HIGH-SCHOOLS. 



% 



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y.SJ 



BY 



WILLIAM G. PECK, Ph.D., LL.D. 



PROFESSOR OF MATHEMATICS, MECHANICS, AND ASTRONOMY, IN COLUMBIA COLLEGE. 



34 J) 









A. S. BARNES & COMPANY, 

NEW YORK AND CHICAGO. 
1883. 



PUBLISHERS' NOTICE. 



PECK'S ACADEMIC AND COLLEGIATE COURSE. 

I.— MANUAL OF ALGEBRA. 
II.— MANUAL OF GEOMETRY. 
III.— TREATISE ON ANALYTICAL GEOMETRY. 
IV.— DIFFERENTIAL AND INTEGRAL CALCULUS. 
V.- POPULAR PHYSICS (From Ganot). 

VI.— ELEMENTARY MECHANICS (Without the Calculus). 
VII.— ELEMENTS OF MECHANICS (With the Calculus). 
VIIL- POPULAR ASTRONOMY. 



Copyright^ 1883, by William G. Peck. 






PREFACE 



rTIHE following work has been prepared to meet the 
wants of the Author, but it is hoped that it will be 
of service not only to other teachers of Astronomy but also 
to the general scientific reader. 

The book is intended to present, in a compact and popu- 
lar form, all the facts and principles of the science that are 
needed in a general course of collegiate education. To this 
end, mathematical formulas and demonstrations have been 
avoided as far as possible, and when it has been deemed 
advisable to introduce them, they have been made incon- 
spicuous by putting them in smaller type. If these sub- 
ordinate paragraphs are omitted, it will be found that the 
remaining ones form a continuous treatise on Astronomy, 
which is as non-mathematical in its character as is con- 
sistent with a scientific treatment of the subject. 

It will be found that the order of arrangement is some- 
what different from that which is met with in most text- 
books. The stars have been treated of in a general way 
before any detailed consideration has been given to the 
solar system ; the descriptions of instruments have been 



IV PREFACE. 

scattered through the book, no instrument being described 
until its use is indicated in the general development of the 
course; an effort has been made to distribute the defini- 
tions of terms so that they shall receive immediate illus- 
tration from the context; and, finally, the various subjects 
considered have been arranged in what seems to be a 
natural and consequently a logical order. It is believed 
that all the changes that have been made are of such a 
character as to secure the early and the continued atten- 
tion of the student. 

The author takes great pleasure in acknowledging his 
obligations to Prof. J. K. Eees, Director of the Columoia 
College Observatory, whose long experience as a teacher of 
Astronomy has enabled him to render much valuable assist- 
ance in the preparation of this work. 

Coixmbia College, j 

September, 1883. \ 



GENERAL CONTENTS. 



PAGE 

I.— Preliminary Principles 7 

II. —Op the Stars : 27 

III.— The Solar System 59 

IV.— The Earth 73 

V.— The Moon 117 

VI. — The Sun and Planets 135 

VII.— Eclipses 175 

VIII.— Of Tides 197 

IX.— Op Calendars 210 

X. — Planets and Satellites 225 

XL— Comets and Meteors 270 

XII.— The Sun and the Stars 313 



ASTRONOMICAL SIGNS. 



1°. Signs of the Zodiac. 



T Aries. 


a 


Leo. 


t 


Saggitarius. 


b Taurus. 


n 


Virgo. 


V? 


Capricornus 


n Gemini. 


=2= 


Libra. 


/w 


Aquarius. 


22 Cancer. 


"1 


Scorpio. 


X 


Pisces. 



2°. Signs of the Sun and Planets. 



O The Sun. 
$ Mercury. 
9 Venus. 



© The Earth. 
6 Mars. 
U Jupiter. 



h Saturn. 

V or $ Uranus. 

¥ Neptune. 



3°. Signs of Position. 

Q Ascending Node. 6 Conjunction 
$ Descending Node. 8 Opposition. 



a Quadrature. 



THE GREEK ALPHABET. 



a Alpha. 


7] Eta. 


v Nu. 


r Tau. 


j3 Beta. 


Theta. 


S Xi. 


v Upsilon. 


y Gamma. 


i Iota. 


o Omicron. 


Phi. 


6 Delta. 


« Kappa. 


77 Pi. 


X Chi. 


e Epsilon. 


A Lambda. 


p Rho. 


V> Psi. 


? Zeta. 


ft Mu. 


<t Sigma. 


(o Omega. 



ASTRONOMY. 



I. PRELIMINARY PRINCIPLES. 

The Heavenly Bodies. 

1. All space is filled with an imponderable substance that 
we call ether. 

This substance constitutes the medium that transmits 
light, by means of which alone we derive all our knowledge 
of objects external to the earth. 

Scattered through this boundless ocean of ether are 
myriads of bodies, of which our earth is one, and these are 
called the heavenly bodies. 

Some of the heavenly bodies are larger than the earth, 
and some are smaller ; some shine by their own light, and 
some by reflected light ; some are solid, and some are gas- 
eous ; but we have reason to believe that they are all in 
motion. The most important of the heavenly bodies are : 
the sun ; the planets, of which our earth is one ; the sat- 
ellites, of which the moon is one; the comets ; the fixed 
stars ; and the nebulae. 

The sun, the fixed stars, and the nebulas are incandescent, 
and shine by their own light; the planets and the satellites 
are dark bodies, and shine by reflected light. 



8 ASTRONOMY. 

Definition of Astronomy. 

2. Astronomy is the science that treats of the heavenly 
bodies. 

Its object is to determine the distances, forms, and mag- 
nitudes of the heavenly bodies ; to explain their motions, 
both real and apparent ; and to investigate, as far as possi- 
ble, their physical conditions. It also embraces an explana- 
tion of the methods of applying the principles of the science 
to the wants of society. 

The Celestial Sphere. 

3. All the heavenly bodies outside of our earth appear as 
though they were fixed on the concave surface of an im- 
mense hollow globe; this surface is called the celestial 
sphere. 

The heavenly bodies are in reality at very different dis- 
tances from us, and the places they seem to occupy are sim- 
ply the points where visual rays drawn through them meet 
the celestial sphere. This surface, on which the heavenly 
bodies are projected by the eye, is purely imaginary, and it 
has been found convenient for the purposes of the astrono- 
mer, to regard its radius as infinite. This supposition ena- 
bles us to consider the centre of the celestial sphere as being 
either at the centre of the earth, or at the centre of the sun, 
inasmuch as the distance of the sun from the earth is insig- 
nificant in comparison with the assumed radius of the celes- 
tial sphere. 

It will be shown hereafter that the shape of the earth is 
ellipsoidal, but for the purposes of description we shall re- 
gard it as spherical, and in most cases we shall regard its 
centre as the centre of the celestial sphere. 

Diurnal Motion. 

4. The entire celestial sphere appears to revolve daily 
from east to west, turning around an axis that passes 



PRELIMINARY PRINCIPLES. 9 

through the centre of the earth. In consequence of this 
apparent rotation, each of the heavenly bodies appears to 
move in a circle whose centre is in the axis of revolution 
and whose plane is perpendicular to that axis. This appar- 
ent rotation of the heavens is called the diurnal motion ; 
the line about which it appears to take place is called the 
axis of the celestial sphere ; and the circles in which the 
heavenly bodies seem to revolve are called diurnal circles. 

The diurnal motion, which is only apparent, is due to the 
actual rotation of the earth from west to east about an 
axis which always maintains a sensibly fixed direction in 
space. The axis of the celestial sphere is therefore the axis 
of the earth prolonged to the heavens. The points in which 
this line meets the surface of the earth are called the poles 
of the earth, and those in which it meets the heavens are 
called the poles of the celestial sphere. That pole, 
either of the earth or of the heavens, which is the nearer to 
an observer in this country is called the north pole, and 
the one opposite to it is called the south pole. 

It is in consequence of the diurnal motion that the sun, 
moon, and stars appear to rise in the east and set in the 
west. 

Definitions. 

5. A vertical line is a line whose direction is indicated 
by a freely suspended plumb-line. 

Every vertical line passes through the centre of the earth, 
and consequently no two vertical lines can be parallel. 

The point in which the vertical line at any place when 
prolonged upward meets the celestial sphere is called the 
zenith of that place, and the point in which it meets the 
celestial sphere when prolonged downward is called the 
nadir of the place. 

6. A horizontal plane is a plane that is perpendicular 
to a vertical line. 

A horizontal plane through any place is called the sensi- 



10 ASTRONOMY. 

ble horizon of that place, and a plane parallel to it through 
the centre of the earth is called the rational horizon of the 
place. 

Because the earth's radius is insignificant in comparison 
with that of the celestial sphere, the circles in which the 
sensible and the rational horizon meet the heavens may be 
regarded as coincident, and for most purposes either one 
may be taken as the celestial horizon. 

7. A vertical plane is a plane that passes through a 
vertical line, and its intersection with the celestial sphere is 
called a vertical circle. 

The vertical plane at any place which passes through the 
axis of the earth is called the meridian plane of that place ; 
its intersection with the surface of the earth is called the 
terrestrial meridian, audits intersection with the heavens 
is called the celestial meridian, or simply the meridian 
of the place. 

The terrestrial meridian of a place passes through the 
poles of the earth ; the celestial meridian passes through 
the poles of the heavens and also through the zenith and the 
nadir of the place. 

The vertical plane which is perpendicular to the meridian 
plane is called the prime vertical. 

The intersection of the horizon by the meridian plane is 
a north and south line ; the intersection of the horizon by 
the prime vertical is an east and west line. 

8. The altitude of a heavenly body is its angular distance 
above the horizon, and its azimuth is the angle between the 
meridian and a vertical circle through the body. 

The zenith distance of a body is its angular distance 
from the zenith. It is the complement of the altitude. 

The altitude and the zenith distance of a body are meas- 



PRELIMINARY PRINCIPLES. 



11 



ured on the vertical circle through the body ; the azimuth 
is measured on the horizon, usually from the south point, 
around by the west through 360°. 



Explanation. In this figure E is the 
centre of the earth and of the celestial 
sphere ; PP' is the axis of the earth and 
of the celestial sphere ; P and P' are the 
poles of the heavens ; EZ is a vertical 
line ; Z is the zenith and Z' is the nadir ; 
HAH' is the horizon ; PH'P' is the meri- 
dian ; ZSZ' is a vertical circle through 
S ; the angle AES, measured hy the arc 
AS, is the altitude of S ; the angle H'EA, 
measured hy the arc H'A, is the azimuth 
of S ; and the angle ZES, measured hy 
the arc ZS, is the zenith distance of S. 



9. The equator is a great 
circle of the earth, whose 
plane is perpendicular to the 
axis. If the plane of the 

equator is extended in all directions, the great circle in which 
it meets the heavens is called the equinoctial. 

The equinoctial is sometimes called the equator of the 
heavens ; it is everywhere equally distant from the poles of 
the celestial sphere. 



?/ 


V 




\ S >v 




~~T~ 


\ 


7 V x\ 




\ 


E 


•v J j 








r^ J 








yOr 



z' 

Fig. 1. Illustration of definitions. 



10. The latitude of a place on the earth is its angular 
distance from the equator. 

The latitude of a place is measured on the meridian of 
that place, and is called north or south latitude according 
as the place is north or south of the equator. The latitude 
of a place is always equal to the angular distance of the 
zenith of the place from the plane of the equinoctial. The 
latitude of either pole is 90°. 



A parallel of latitude is a small circle of the earth 
whose plane is parallel to the equator. 
All places on the same parallel have the same latitude. 



12 



ASTRONOMY. 




<r 



'?' 



Fig. 2. 



Explanation. Figure 2 represents 
the projection of the celestial sphere 
on the plane of the meridian of the 
place a ; PP' is the axis of the earth 
and of the heavens ; EZ is the vertical 
at a ; pqp' is the terrestrial meridian of 
the place a ; PQP' is the celestial meri- 
dian ; qq' is the projection of the equa- 
jK tor, and QQ' that of the equinoctial; 
HH is the projection of the horizon ; 
aa' is the projection of the parallel of 
latitude through a : qEa, equal to QEZ, 
is the latitude of a ; and PEZ, equal 
90° -QEZ, is the co-latitude of a. 

It is to be remembered that EZ is in- 
finitely great in comparison with Ea, 
and consequently that HH is the celes- 
tial horizon of a. 



The Sun's Apparent Motions. 

11. The sun has an apparent diurnal motion like the 
fixed stars, and in addition it has an apparent motion from 
ivest to east amongst the stars by virtue of which it seems 
to complete an entire circuit of the heavens in a period we 
call a year. The apparent annual path of the sun amongst 
the stars, which is a great circle of the celestial sphere, is 
called the ecliptic. 

The ecliptic retains a fixed position with respect to the 
stars, and cuts the equinoctial in two points called equi- 
noxes. The point at which the sun passes from the south to 
the north side of the equinoctial is the vernal equinox, and 
the point at which it passes from the north to the south side 
of the equinoctial is the autumnal equinox. The sun is 
at the vernal equinox about the 21st of March, and at the 
autumnal equinox about the 22d of September. 

The term eqvinoxes is applied, not only to the points as above de- 
fined, but also to the dates at which the sun passes them. A like 
amplication is made of the term solstic3S, yet to be defined. 



The angle between the planes of the ecliptic and the 



PRELIMINARY PRINCIPLES. 13 

equinoctial, which is about 23° 27', is called the obliquity 
of the ecliptic, and the line in which these planes inter- 
sect is called the line of equinoxes. 

The sun's apparent diurnal motion is due, as explained 
in Art. 4, to the earth's rotation on her axis. In like man- 
ner his apparent motion amongst the stars is due to an 
actual motion of the earth. The sun is the fixed bod}' and 
the earth makes an annual revolution around him, moving 
from west to east in a path, or orbit, which determines the 
plane of the ecliptic. The sun's apparent place in the 
heavens is always on the prolongation of a visual ray drawn 
from the earth to the sun ; hence, when the earth revolves 
around the sun from west to east, the prolongation of the 
visual ray revolves in the same way, that is, the sun appears 
to revolve in the same direction that the earth actually 
revolves, and with the same angular velocity. The ecliptic 
is therefore the great circle of the celestial sphere, in which 
the plane of the earth's orbit indefinitely extended meets 
the heavens. 

It will often be found convenient to speak of the apparent motions 
of the sun, both diurnal and annual, as though they were real ; and no 
error can result from this form of expression, if the explanations 
already given are carefully borne in mind. 



Precession of the Equinoxes. 

12. The equinoxes have a slow, but not quite uniform, 
motion from east to west along the ecliptic, that is, in a 
direction contrary to that of the sun in its annual path. 
This motion, which on an average is equal to 50".2 a year, 
is called the precession of the equinoxes. 

The precession of the equinoxes gives rise to a slow 
change in the direction of the earth's axis, by virtue of 
which the poles of the heavens circle around those of the 
ecliptic in an enormous cycle of more than 25,000 years. 



14 ASTRONOMY. 

The cause of the precession, and its effects on the aspect of the visi< 
ble heavens, will be more fully treated of in a subsequent article. 

Additional Definitions. 

13. The solstices are the points of the ecliptic that are 
midway between the equinoxes. The one that is north of 
the equinoctial is called the summer solstice, and the 
one that is south of the equinoctial is called the winter 
solstice. 

The solstices, which are 90° distant from the equiuoxes, 
are the points of the sun's annual path that are farthest 
from the equinoctial. The sun is at the summer solstice 
about the 21st of June, and at the winter solstice about the 
21st of December. In either case its angular distance from 
the equinoctial is equal to the obliquity of the ecliptic, that 
is, to abou| 23° 27'. 

14. An hour circle is a great circle of the celestial 
sphere which passes through the poles of the heavens. It 
is also called a declination circle. 

The hour circle that passes through the equinoxes is 
called the equinoctial colure, and the hour circle that 
passes through the solstices is called the solstitial colure. 

The meridian of a place is an hour circle ; that half of it 
which stretches from pole to pole and which passes through 
the zenith of the place is called its Tipper branch, and the 
remaining half is called its lower branch. When a heav 
enly body, in its diurnal motion, appears to cross the meri- 
dian of the place of the observer, it is said to culminate. 
The passage of a body over the upper branch of the me- 
ridian is called its upper culmination, or its upper 
transit ; its passage over the lower branch is called its 
lower culmination, or its lower transit. The term 
culmination, when used by itself, is understood to mean the 
upper culmination* 



PRELIMINARY PRINCIPLES. 



15 



The term hour circle of a body is frequently used in a limited sense 
to mean that half of the hour circle which extends from pole to pole 
and passes through the body. The context shows wheu the term is 
used in this sense. The term meridian is also used in the same sense. 



15. The hour angle of a body is the angle between the 
meridian of the place and the hour circle of the body. 

The hour angle is measured on the equinoctial. If the 
body is west of the upper branch of the meridian, its hour 
angle is positive ; if the body is east of the meridian, its hour 
angle is negative. Thus, the hoitr angle of the sun is nega- 
tive in the morning and positive in the afternoon. 



Explanation. The circle QRQ,' is the 
equinoctial ; P and P' are the poles of the 
heavens ; KVK' is the ecliptic and T,T' are 
its poles ; V is the vernal and A is the au- 
tumnal equinox; K is the summer and K' 
is the winter solstice ; the angle QEK 
measured by the arc QK is the obliquity of 
the ecliptic ; PVP'A is the equinoctial col- 
ure ; PQP'Q' is the solstitial colure ; PSR 
is part of the hour circle of the body S ; 
and the angle QPR, measured by the arc 
QR, is the hour angle of S. The direction 
of the sun's apparent annual motion is in- 
dicated by the arrow. The solstitial colure 
passes through the poles of the heavens 
and also through the poles of the ecliptic. 
The arc PT is equal to 23° 27'. 




Illustration of definitions. 



Right Ascension and Declination. 

16. The right ascension of a heavenly body is the arc 
of the equinoctial included between the vernal equinox and 
the hour circle of the body. Thus, in Fig. 3 the arc VK is 
the right ascension of the body S. 

Right ascensions are reckoned from west to east, counting 
from the vernal equinox around through the entire circle 
of the equinoctial. They may be expressed in degrees, mi?i- 
utes, and seconds of angular measure, but for reasons yet to 



16 ASTRONOMY. 

be explained it is found more convenient to express them in 
hours, minutes, and seconds, each hour corresponding to 15° 
of arc, each minute to 15' of arc, and each second to 15" 
of arc. 

The declination of a heavenly body is its angular dis- 
tance from the plane of the equinoctial. Thus, in Fig. 3, 
the angle KES, measured by the arc RS, is the declination 
of the body S. 

Declinations are always expressed in degrees, minutes, 
and seconds of angular measure, and are reckoned on the 
hour circle that passes through the body in question. If 
the body is north of the equinoctial, its declination is re- 
garded as positive; if it is south of the equinoctial, its 
declination is negative. 

The polar distance of a body is its angular distance 
from the north pole of the heavens. Thus, in Fig. 3, PES, 
measured by the arc PS, is the polar distance of the body S. 

The polar distance of a body is equal to 90° minus the 
body's declination. Thus, the polar distance of a body 
whose declination is +23° 27 'is 66° 33', and the polar dis- 
tance of a body whose declination is —23° 27' is 113° 27'. 
From what has been explained it is obvious the sun's polar 
distance varies between the limits 66° 33' and 113° 27'. 

The right ascension and the declination of a body determine its 
position on the celestial sphere in the same way that the longitude 
and the latitude of a place determine its position on the surface of the 
earth. These elements of reference are determined by means of the 
astronomical clock and the transit circle. 



Sidereal Time. 

17. The interval between two successive culminations of 
the same star over the upper branch of the meridian of any 
place is called a sidereal day. The sidereal day is divided 
into 24 equal parts called hours, each hour is divided into 



PRELIMINARY PRINCIPLES. 17 

60 equal parts called minutes, and each minute is divided 
into 60 equal parts called seconds. Time reckoned in terms 
of these units is called sidereal time. 

The sidereal day, which is assumed to be of invariable 
length, is the fundamental unit of astronomical time. The 
meridian of any place is carried from west to east with the 
earth as it turns on its axis, and setting out from any star 
its upper branch will sweep over every star of the heavens 
and return to its first position in the time required for the 
earth to turn once on its axis. Hence, the sidereal day is 
equal to the time required for the earth to revolve on its 
axis ; it is also equal to the time required for any star to 
make a complete revolution in its diurnal circle. 

The diurnal rotation of the earth takes place uniformly ; 
hence, it turns through any fractional part of 360° in the 
same fractional part of a sidereal day. It will therefore 
revolve through an angle of 15° in a sidereal hour, through 
an angle of 15' in a sidereal minute, or through an angle 
of 15" in a sidereal second. This relation enables us to 
convert angular expressions into equivalent expressions in 
time, and the reverse, operations that are often required in 
astronomical computations. 

The sidereal day used in practiced astronomy begins when the ver- 
nal equinox is on the upper branch of the meridian of the place of 
observation. The practical sidereal day is therefore a trifle shorter 
than the sidereal day above described. For, while the meridian, start- 
ing from the vernal equinox, is moving eastward, the equinox itself is 
moving slowly toward the west in consequence of precession ; conse- 
quently, the meridian will meet the equinox before it completes an 
entire revolution, that is, the sidereal day in actual use is a little less 
than the time required for the earth to make a complete revolution on 
its axis. The difference, which is less than a hundredth part of a 
second, is so small that it may be disregarded in a popular exposition 
of astronomical principles. 

From what has been said above it is obvious that the 



18 ASTRONOMY. 

sidereal time at which any body crosses the meridian is the 
same as the right ascension of the body expressed in time. 

The Astronomical Clock. 

18. An astronomical clock is a clock that is adjusted so 
as to keep accurate time. It differs but little from an ordi- 
nary clock except in nicety of construction. Its dial-plate, 
however, is usually divided into 24 equal parts, and its 
mechanism is such that the hour-hand turns around the 
dial once in 24 hours. The clock may be made to keep 
sidereal or solar time ; when used as a sidereal clock, the 
pendulum is made of such length that the hour-hand shall 
make one revolution in a sidereal day. The most important 
parts of an astronomical clock are the pendulum and the 
escapement. The pendulum is compensating (Mech. Arts, 
118-120), and the escapement is so constructed as to offer 
a minimum resistance to uniformity of motion. 

It is not necessary that a sidereal clock should be set so 
as to indicate Oh. 0m. 0s. when the vernal equinox is on 
the meridian, provided we know its error, neither is it 
necessary that it should turn through exactly 24 hour 
spaces in a sidereal day, provided its gain or its loss in equal 
times is always the same. 

The error of a clock at any given time, or epoch, taken 
with its proper sign, is called the correction; if the clock 
is fast, the correction is — ; if slow, it is +. The amount 
that it gains or loses per day is called the rate ; if it gains, 
the rate is — ; if it loses, it is + . 

Knowing the correction at a given time or epoch, and the rate, we 
may find the correction at any subsequent time by the following Rule : 

Multiply the rate by the number of days and deci- 
mal parts of a day since the epoch, and apply the 
result, with its proper sign, to the given correction ; 
the result will be the required correction. 



PRELIMINARY PRINCIPLES. 



19 



Example. At 12h. sidereal time, June 17th, a clock was 7m. 
38s. fast, and it was losing 4s. a day ; what was its error at 18h. side- 
real time, June 29th ? 

Operation. — 7m. 38s. -f- 4s. x 12.25 = — 6m. 49s., correction ; 
hence, 6m. 49s. must be subtracted from the reading of the clock to 
get the true time. 

The Astronomical Telescope. 

19. The ordinary refracting telescope, in its simplest 
form, consists of two lenses set in the opposite ends of a 
suitable tube. The larger lens, called the objective, receives 
the rays of light coming from a distant object, and so con- 
verges them as to form an image of that object ; the smaller 
one, called the eye-piece, is used as a magnifier to view the 
image thus formed. 

In modern telescopes the objective consists of two lenses 
placed close together ; the outer one, which is of crown 
glass, is convex, that is, it 
is thicker at the middle than 
at the edge ; the inner one, 
which is of flint glass, is 
concave, that is, it is thin- 
ner at the middle than at 
the edge. The curvatures 
of the surfaces of the two 
lenses are so chosen that 
the compound lens will give 
a distinct image free from 
color ; in this case the ob- 
jective is said to be achro- 
matic. 

The eye-piece is composed of two convex lenses (usually 
plano-convex) placed a little distance apart ; the one next 
the objective is called the field-lens, and the one next the 
eye is called the eye-lens. The lenses may be so arranged 
that the image of an object shall fall between the lenses, in 
which case the eye-piece is said to be negative ; or they 



'— *■ 



> A 




Fig. 4. Section of achromatic objective. 
A is a convex, and B is a concave lens, 
A being turned toward the object. 



20 ASTKONOMY. 

may be so placed that the image shall fall in front of the 
field-lens, that is, between it and the objective, in which 
case the eye-piece is said to be positive. 



Explanation. The lenses are of nearly 
equal focal lengths, and the distance be- 
tween them is about f the focal length of 
either. In this case the focal length of the 
combination is not far from f the[focal length 
of either lens. 



Fig. 5. section of positive eye- When the telescope is used 

piece. C is the field-lens, and T> . , . ' . , . , 

the eye-lens. simply to view an object, the 

negative eye-piece is preferred ; 
but when it is used to fix the exact direction of a body, the 
positive eye-piece is employed. The objective and the eye- 
piece should be so arranged in the tube that their axes 
shall coincide with each other and with the axis of the 
tube. 



20. In a telescope to be used for measurements, the cen- 
tre of the field of view is shown by the intersection of two 
fine lines, called cross-hairs. These lines are attached to a 
perforated diaphragm, provided with suitable adjusting 
screws for bringing the intersection of the cross-lines into 
its proper position. The line joining the optical centre of 
the objective with the intersection of the cross-hairs is the 
line of collimation. When the instrument is ready for use, 
the plane of the cross-hairs is at the common focus of the 
objective and the eye-piece. If the image of a star is seen 
at the intersection of the cross-hairs, the star itself must be 
in the prolongation of the line of collimation, for the ray of 
light that coincides with the line of collimation passes 
through the objective without deviation. 

In the transit instrument, yet to be described, the dia- 
phragm carries a system of hairs or wires, which is some- 
times called a reticle. The manner in which the wires are 
arranged is shown in the figure. The wire dc is horizontal, 



PRELIMINARY PRINCIPLES. 



21 




Fig. 6. The reticle. 



and is sometimes double. The wires at right angles to dc 
are equidistant and usually either 5 or 7 in number, the 
middle one, ab, intersecting the hori- 
zontal one, dc, in the line of colli ma- 
tion. At whatever elevation the line 
of collimation may be set, the middle 
wire of the parallel system will be in 
the plane of the^ meridian, and the 
times required for a star to pass from 
wire to wire will be sensibly the same 
throughout the system. 

The magnifying power of a tele- 
scope such as we have described is equal to the focal length 
of the objective divided by the focal length of the eye-piece. 
By using eye-pieces of different focal lengths, the magnify- 
ing power of the same telescope may be changed to meet 
the wishes of the observer. 

The capacity of a telescope to bring faint objects into 
view depends upon the size of the objective. The quantity 
of light that falls upon the objective varies with, the square 
of its diameter, and if none is lost either by absorption or 
from faulty construction, the quantity that enters the eye 
will be to the quantity that would enter it without the tele- 
scope as the square of the diameter of the objective is to 
the square of the diameter of the pupil of the eye. 



The Reflecting Telescope. 

21. Besides the kind of telescope already described, there 
is another class in which the image of the object to be viewed 
is formed by means of a curved mirror; these are called 
reflecting telescopes. 

An example of this species of telescope is shown in Fig. 7, 
which represents the great silver-on -glass reflector at the 
Paris observatory. It consists of a tube about 25 feet long, 
at the bottom of which is a curved mirror nearly 4 feet in 



22 



ASTRONOMY. 



diameter. The reflected rays, which would come to a focus 
near the top of the tube, are turned in a lateral direction 
by a small plane mirror, and an image is formed that can 
be viewed by a suitable eye-piece as shown in the figure. 




Fig. 7. Great silver-on-glass Reflector of the Paris Observatory. 

This instrument is equatorially mounted, that is, it 
may be turned around either of two axes, one of which is 
parallel to the axis of the heavens, and the other to the 



PRELIMINARY PRINCIPLES. 23 

plane of the equinoctial. The former, which is the princi- 
pal axis shown in the figure, is called the polar and the 
latter is the declination axis of the instrument. By 
turning the instrument around its declination axis it may 
be set to the declination of any star, and then by turning 
it around the polar axis it may be made to follow the star 
in its diurnal motion. The latter motion is imparted by 
a train of clock-work. 

The Transit Instrument. 

22. A transit instrument is an instrument for de- 
termining when a heavenly body is on the meridian of a 
place. 

It consists essentially of a telescope having an axis at 
right angles to its length, on which it can revolve in such 
manner that its line of collimation shall always be in the 
plane of the meridian. The telescope is provided with a 
reticle like that explained in Art. 20, which can be so 
adjusted as to make the line of collimation perpendicular 
to the axis of rotation, the wire dc being horizontal. The 
axis of rotation of the telescope is terminated at its ex- 
tremities by two equal cylindrical pivots which rest in 
metallic pieces called Y's, and the Y's themselves are sup- 
ported by two piers, between which the telescope revolves. 
One of the Y's can be moved up and doton, and by means 
of a portable level the axis of rotation can be made horizon- 
tal ; the other Y can be moved north and south, and by 
means of astronomical observation the axis can be placed 
due east and west. 

When the axis of rotation is horizontal and also due east 
and west, it must be perpendicular to the plane of the me- 
ridian ; then, if the line of collimation is perpendicular to 
the axis, it is obvious that this line will remain in the plane 
of the meridian when the instrument is revolved in the Y's. 
The line dc of the reticle being parallel to the horizon, the 



24 



ASTRONOMY. 




remaining wires must be parallel 
to the plane of the meridian. 
When the image of a heavenly 
body is on the middle wire of the 
parallel system the body itself 
must be on the meridian of the 
place. 

Explanation. The projection of a transit 
instrument on a vertical plane perpendicular 
to the meridian. AB is the telescope ; CD its 
axis of rotation ; EF the supporting piers ; 
GH the Y'|3 ; KL the pivots ;- the line of col. 
limation revolves around KL, always remain- 
ing in the plane of the meridian. 



Pig. 8. The Transit Instrument. 



Method of Finding Right Ascensions. 

23. The right ascension of a heavenly body is found by 
means of a transit instrument and an astronomical clock. 
The operation consists in finding the exact sidereal time at 
which the body crosses the upper branch of the meridian. 

The telescope of the transit instrument is turned around 
its axis of rotation till it has nearly the proper elevation, 
and when the body enters the field of view, the telescope is 
raised or depressed till the body appears to move along the 
horizontal wire. At the instant the body crosses each of the 
other wires, the reading of the clock is noted. The average 
of all these readings, corrected for the error and the rate of 
the clock, is the sidereal time that has elapsed since the 
vernal equinox was on the meridian, that is, it is the right 
ascension of the body expressed in time. 

If the observation is made on a star when it is on the 
lower branch of the meridian, as it is when the star lies below 
the north pole of the heavens, the exact sidereal time of 
transit must be increased by 12 hours. If this result exceeds 
24 hours, it must be diminished by that amount. 



PRELIMINARY PRINCIPLES. 



25 



The Meridian Circle. 

24. The meridian circle differs but little from the 
transit instrument, except in haying a graduated circle 
attached to its axis of rotation whose centre is in that axis 
and whose plane is perpendicular to it. The telescope and 
the circle revolve together, and the angle through which 
the telescope turns is shown by the arc of the graduated 
circle that sweeps past a fixed index. 

Explanation. The figure represents 
the projection of a meridian circle on 
the plane of the meridian, the nearer or 
western pier heing omitted. L is the 
rotation axis of the telescope AB ; E is 
the remote or eastern pier; ab is the 
graduated circle firmly attached to the 
axis L ; and d is the fixed index. 

If we first take the reading 
of the circle shown by the in- 
dex d when the line of colli- 
mation has the position LA, 
and again take the reading 
of the circle shown by d after 
the telescope has been turned 
till its line of collimation has 
the position LA', the former 
reading subtracted from the latter will give the length of 
the graduated arc that has swept past d during the motion, 
and this will be the measure of the angle ALA'. 

Inasmuch as the circle and telescope turn together, the 
reading of the circle will always be the same when the tele- 
scope has the same direction. The reading when the tele- 
scope is directed toward the pole of the heavens, and which 
we may call the polar reading, can be found as follows : 
direct the line of collimation to a star that is very near the 
pole at the instant of its upper culmination, and take the 
reading of the circle ; then, after an interval of 12 hours, 
direct the line of collimation to the same star at the instant 




Fig. 9. The meridian circle. 



26 ASTRONOMY. 

of its lower culmination, and take the reading of the circle ; 
the half sum of these readings (after both are corrected for 
atmospheric refraction) will be the polar reading. 

If we subtract 90° from the polar reading we have what 
may be called the equinoctial reading, that is, the reading 
of the circle when the line of collimation is in the plane 
of the equinoctial. 

Method of Finding Declinations. 

25. The declination of a heavenly body is found by means 
of the meridian circle. The operation consists in finding 
the reading of the circle when the line of collimation of the 
telescope is directed to the body at the instant of its upper 
culmination. 

As the body approaches the meridian, the telescope of the 
meridian circle is turned on its axis of rotation till the line 
of collimation has nearly the proper elevation, and when the 
body enters the field of view the instrument is elevated or 
depressed till the body seems to move along the horizontal 
wire. When the body reaches the middle vertical wire the 
reading of the circle is taken at the index d ; this reading, 
corrected for atmospheric refraction, and then diminished 
by the equinoctial reading, is the required declination. 

If the reading found is greater than the equinoctial 
reading, the difference will be positive, and the declination 
north ; if the reading found is less than the equinoctial 
reading, the difference will be negative, and the declination 
south. 

The descriptions given in this and in the preceding articles are only 
intended to impart a general notion of the instruments used, and of 
the methods employed in finding the right ascensions and declinations 
of the heavenly bodies ; more detailed accounts belong to the subject 
of practical astronomy. 



/ 



II. OF THE STARS. 

Classification of Stars. 



26. The fixed stars are divided into classes according to 
their apparent brightness ; the brightest stars are said to be 
of the first magnitude, those next in order of brightness 
are said to be of the second magnitude, and so on down 
to the faintest that can be seen with the naked eye by the 
ordinary observer, which are usually classed as stars of the 
sixth magnitude. Still fainter stars are rendered visible 
by the aid of the telescope, and the same method of classi- 
fication is continued to the sixteenth magnitude, be- 
yond which it is seldom extended. 

This method of classification is perfectly arbitrary, and 
astronomers are by no means agreed as to the classes to 
which certain stars are to be assigned. Amongst those of 
the same magnitude, also, very great differences of bright- 
ness exist, more even than between some that are classed 
in different magnitudes. The lines of division between the 
stars of the different magnitudes are the result of usage. 
According to Sir John Herschel there are 23 or 24 stars of 
the first magnitude, from 50 to 60 of the second magnitude, 
about 200 of the third magnitude, and so on, the numbers 
in each class increasing very rapidly as we descend in the 
scale of brightness. He estimates that the entire number 
of stars included in the first seven magnitudes is between 
12,000 and 15,000. The number of stars in the remaining 
classes are counted by millions. 

Astronomers are sometimes in doubt as to which class a 
star belongs, and in such cases it has been the practice to 
place it between two classes ; thus, if a star is between the 
second and third magnitudes, it is numbered 2*3 or 3 '2. 



2S ASTRONOMY. 

Both of these signs indicate that the star in question is 
between the second and third magnitudes, the former de- 
noting that it is nearer the second, and the latter that it is 
nearer the third magnitude. 

Catalogues of Stars. 

27. A catalogue of stars is a tabular statement of the 
right ascensions and declinations of certain stars together 
with their several magnitudes. 

Numerous star catalogues have been published, but the most ex- 
tensive one is that of Argelander, which contains, approximately at 
least, the places of all the stars down to the ninth magnitude, and 
lying between the north pole of the heavens and a diurnal circle 2° 
south of the equinoctial. This catalogue has been extended in the 
southern hemisphere by Dr. Gould of the Cordova Observatory, in 
South America, and the entire catalogue now embraces more than half 
a million of stars. Catalogues like this are of great value to the 
astronomer, but others of greater accuracy, though containing fewer 
stars, are found to be more generally useful. Perhaps the most valu- 
able one of the latter class is the British Association Catalogue, which 
gives the positions of more than 8,000 stars. 

Star Maps and Celestial Globes. 

28. When we know the right ascensions and declinations 
of the principal stars, we can show their relative positions 
and groupings by plotting them either on a plane surface 
or on the surface of a sphere. In the former case we have 
a star map and in the latter a celestial globe. 

Star maps and celestial globes are constructed on the 
same general principles as terrestrial maps and globes, hour 
circles in the former corresponding to meridians in the lat- 
ter, and diurnal circles in the former to parallels of latitude 
in the latter. 

Terrestrial maps represent the relative positions of objects as seen 
from above, whereas star maps represent them as seen from below. 
Hence, for regions south of the pole the top of the map is north, and 



OF THE STARS. 



29 



the right hand is west ; for regions north of the pole the top of the 
map is south, and the right hand is east. In like manner a celestial 
globe represents the relative positions of the stars as they would ap- 
pear to an observer at its centre and looking outward. In using a star 
map, therefore, we imagine it to he placed between the eye and that 
part of the heavens which it represents ; in using a celestial globe, we 
suppose the eye to be placed at its centre. 

The configurations of star groups are always the same, 
but in consequence of the motion of the observer the line 
joining any two stars is continually changing its apparent 
direction ; hence it is impossible to point out the direction of 
one star from another in the same manner that we indicate 
the direction of one place from another on the surface of the 
earth. This is shown in Fig. 10, which represents the group 
of stars that is commonly called the dipper in different posi- 
tions as it circles around the pole. 



Explanation. . Figure 
10 shows the positions of 
the dipper (a part of the 
great hear) as it appears at 
different seasons. A is its 
position at 9 o'clock on the 
loth of May ; B is its posi- 
tion at 9 o'clock on the 
15th of August; C is its 
position at 9 o'clock on the 
15th of November ; and D 
is its position at 9 o'clock 
on the 15th of February. 






f*\ \ 



* B 






> k + + 






G 

* * X 



Of two stars which 
are near together and 
on the same side of 
the pole, that is said to 
be most northerly 
which lies nearer the 
north pole; that 
which comes to the 
meridian first is said 
to 'precede, and the other one is said to follow. These terms are often 
used to describe the position of one star with respect to another ; 



H0F1Z0I\. 

Fig. 10. Circumpolar stars. 



30 ASTRONOMY. 

thus, if we say that the star A is south following the star B, we mean 
that the star A is further from the north pole than the star B, and that 
A crosses the meridian after B. 



Constellations. 

29. The stars are not uniformly distributed over the 
heavens, but are aggregated in groups, whose boundaries 
are more or less distinctly outlined. These groups, which 
are called constellations, were recognized by the earliest 
astronomers, and many of them still bear names that were 
given to them as long ago as the time of Hipparchus. 

The earlier star maps and globes were covered with rude 
figures of men and animals, each of which stood for a par- 
ticular constellation ; such figures are passing into disuse, 
and the names of the constellations are now used simply to 
indicate certain portions of the heavens. The boundaries 
of the constellations are usually laid down on the map or 
globe, and to a certain extent they afford a convenient means 
of referring to particular stars. In the same way that it 
is easier to describe Washington as the capital of the United 
States, than to say that its longitude is 5h. 8m. W. and its 
latitude is 38° 53' N., so it is easier to describe Eegulus as 
the principal star in the constellation Leo, than to say its 
right ascension is lOh. 2m. and its declination is 12° 33' N. 

Astronomers do not entirely agree as to the boundaries, 
nor even as to the number of the constellations. There 
were 48 ancient constellations, but these did not cover the 
entire celestial sphere, and others have been added in 
modern times ; some of the latter have not been accepted 
by astronomers. According to Proctor there are now 84 
recognized constellations, which may be divided into three 
classes, viz. : zodiacal, northern, and southern constellations. 
Of these, some are so near the south pole as to be either 
wholly or nearly invisible to an observer in the latitude of 
New York. Others are comparatively insignificant, either 



OF THE STARS. 31 

on account of their small size, or because of the faintness of 
the stars embraced within their limits. 

Names and Designations of Stars. 

30. The earlier astronomers gave particular names to the 
principal stars, and some of these are yet in general use. 

Thus, the principal star in the constellation Cants Major 
is called Sirius, the principal star in Taurus is Aldebaran, 
that in Lyra is "Vega, and so on. 

Bayer introduced the plan now in use, of designating the 
stars in each constellation by letters of the Greek alphabet, 
using Roman letters and numbers when the Greek letters 
were exhausted. The brightest star in each constellation is 
called a, the next brightest 13, and so on. Thus, the bright- 
est star in the constellation Leo is called a Leonis, the next 
brightest /? Leonis, and so on. In some cases, however, the 
order of brightness is not indicated by the order of the let- 
ters employed. 

The Zodiac and Zodiacal Constellations. 

31. The zodiac is a zone or belt extending about 8° both 
north and south of the ecliptic. This belt is of importance 
only because it embraces the apparent paths of the sun, the 
moon, and the principal planets. 

The ecliptic and the zodiac are divided into 12 equal parts 
called signs. The names of the signs, beginning at the 
vernal equinox and counting from west to east, together 
with their English equivalents and the characters by which 
they are denoted, are as follows : Aries, the ram, T ; 
Taurus, the hull, b ; Gemini, the twins, n ; Cancer, 
the crab, 25 ; Leo, the lion, SI ; Virgo, the virgin, ty ; 
Libra, the balance, === ; Scorpio, the scorpion, fll ; Sagit- 
tarius, the archer, $ ; Capricornus, the goat, V? ; Aqua- 
rius, the waterman, ~; and Pisces, the fishes, X. 

The zodiacal constellations have the same names as 



32 ASTRONOMY. 

the signs of the zodiac, but are not coincident with them. 
When the constellations were named it is probable that 
each coincided very nearly with the sign of the same name, 
but in consequence of the precession of the equinoxes the 
signs of the zodiac have fallen back with respect to the 
stars, till now, after the lapse of 2000 years, the constella- 
tion Aries has come to coincide very nearly with the sign 
Taurus, the constellation Taurus with the sign Gemini, and 
so on. This would seem to indicate that the zodiacal con- 
stellations were named more than a hundred years before 
the beginning of the Christian era. 

Northern and Southern Constellations. 

32. The northern constellations are those that lie 
between the zodiac and the north pole of the heavens. 
The most important of these are, Ursa Major, the great 
bear ; Ursa Minor, the little bear ; Draco, the dragon ; 
Cepheus ; Cassiopeia ; Camelopardus, the giraffe ; 
Bootes ; Corona Borealis, the northern croivn ; Her- 
cules ; Lyra, the lyre ; Cygnus, the swan ; Perseus ; 
Auriga, the waggoner ; Serpentarius or Ophiuchus, 
the serpent bearer ; Serpens, the serpent; Aquila, the 
eagle ; Delphinus, the dotyhin ; Pegasus ; and An- 
dromeda. 

The first six of the constellations above named are said to 
be circwnpolar, that is, they circle around the pole without 
sinking below the horizon. i 

The southern constellations are those that lie be- 
tween the zodiac and the south pole of the heavens. The 
mqsfc important of these, that are wholly or for the most 
part visible in the latitude of New York, are Cetus, the 
wliale ■; Orion ; Canis Major, the great dog ; Canis 
Minor, the little dog; Crater, the cup; Corvus, the 
crow ; Eridanus, the river Eridanus ; and Piscis Aus- 
tralis, the southern fish. The principal constellations 



OF THE STAKS. 33 

that are invisible in our latitude are Argo Navis, the 
ship Argo; Hydra; Centaurus, the centaur ; Lupus, 
the wolf ; Corona Australis, the southern crown ; and 
Crux Australis, the southern cross. 

The minor constellations, both northern and southern, 
may be found on any good celestial globe. 

The student should familiarize himself with the location, and the 
names of the leading stars, of the principal constellations. This is 
most readily accomplished by the aid of a celestial globe. 

The Star Maps. 

33. A preliminary notion of the general location of some 
of the most important constellations may be obtained from 
the following miniature maps and the accompanying de- 
scriptions. 

Method of Using the Maps. — Map I. is to be held so 
as to be perpendicular to a line from the eye to the pole star, 
and then turned around till the constellations on the map 
and in the heavens have corresponding positions with re- 
spect to the meridian. At 9 o'clock in the evening of May 
loth the vertical line through the middle of the map will 
coincide very nearly with the meridian ; at other* times the 
map must be turned around till the middle vertical line 
passes through Polaris and y Ursas Majoris. Maps II., III., 
IV., and V. are to be held so that the middle vertical line of 
each shall coincide with an hour circle, the top of the map 
being toward the north. At 9 o'clock in the evening of the 
day named on any map the middle vertical will coincide 
with the meridian ; at other times the map must be turned 
around till it corresponds in position with the stars that it 
represents. It is to be noted that the right hand side of 
each of the last four maps lies to the ivest and the left hand 
side to the east, just the reverse of what obtains in a terres- 
trial map. 



34 ASTRONOMY. 

Method of Tracing out the Constellations. 

34. The great bear. The seven principal stars of this 
constellation form a group that is commonly known as the 
Dipper. This group circles around the north pole of the 
heavens, as shown in Fig. 10. The star nearest the pole is 
called a, and the other stars of the group, taken in order, 
are called ft y, d, e, £, and ?/, as shown in Map I. 




Fig. 11. Map I., May 15th, 9 o'clock p.m. 

This constellation gives us two convenient measures which are of 
continual use in estimating distances in the heavens : the distance 
from a to /3 is about 5°, and the distance from a to rj, that is, the en- 
tire length of the dipper, is about 25°. 



OF THE STARS. 35 

The little bear. The stars a and (5 of the great bear are 
called pointers, because the line from (3 to a, when pro- 
longed about 30°, passes through the pole star, which is 
the principal star in the little bear. This star is called 
a Ursa? Minoris, or more commonly Polaris, and it is the 
star around which all the other stars appear to revolve. 
The seven principal stars of this constellation also form the 
figure of a dipper, but its handle is curved in a different 
way from that of the other dipper, as shown in Map I. 

The handles of the two dippers, which correspond to the tails of the 
two bears, are turned toward opposite points of the heavens. 

Cassiopeia. A line from <S Ursae Majoris to the pole 
star, and then prolonged as much farther, goes to the star 
j3 in Cassiopeia. The five principal stars of this constella- 
tion form a figure shaped like a wide W, having its top 
toward the pole. The Greek letters that designate these 
stars, taken in order, form the word /3ayde, as shown on 
Map I. 

Cepheus. A line drawn from a to Cassiopeia?, and 
then prolonged about four times its own length, goes to 
the principal star in Cepheus, which is called a Cephei ; 
£ Cephei is on a line from a toward Polaris, and is about 
7° from the former ; 6 Cephei lies at the vertex of a nearly 
equilateral triangle, whose other vertices are a and /?. The 
other stars of this constellation may be learned from the 
map. 

Draco. A line from 6 Cassiopeia? to (3 Cephei, when 
prolonged a distance equal to itself, goes to the Head of 
the Dragon, which is marked by 4 stars arranged in the 
form of a lozenge. Starting from the head, the remaining 
principal stars form a figure shaped somewhat like the let- 
ter Z and enclosing the constellation Ursa Minor. The 
lower line of the Z lies midway between the two bears, and 
is parallel to the tail of the great bear. 



36 ASTRONOMY. 

Andromeda. If a line is drawn from Polaris to (3 Cas- 
siopeia, and prolonged an equal distance, it will go to a An- 
dromedae, and in like manner if a line is drawn from Polaris 
to e Cassiopeiae, and prolonged an equal distance, it goes to 
y Andromedae. The star (3 lies nearly midway between a 
and y. Knowing then these, the other stars of the constel- 
lation may be found by means of Map IT. 




Fig. 12. Map II, 9 o'clock p.m., December 1st. 



Perseus. A line from (3 to y Andromedae, when pro- 
longed an equal distance, reaches a Persei. At a distance 
of about 10° nearly south of a is j3 Persei, or Algol, a noted 
variable star. The stars a and j3 Persei with y Andromeda? 
form a triangle, right-angled at (3 Persei. The other prin- 
cipal stars of Perseus may be found from the map. 



OP THE STARS. 



37 



Auriga. If we draw a perpendicular to the line joining 
Polaris and « Cassiopeiae at its middle point, and prolong it 
on the side of Perseus, it will pass through Capella, the 
brightest star of Auriga. This star is about 45° from the 
pole. If the line from 6 Persei to a Aurigae is prolonged it 
goes to (3 Aurigae, a star of the second magnitude. The 
other stars of this constellation can be found by the aid of 
Maps III and I. 




Fig. 13. Map III., 9 p.m., March 1st. 



Taurus. Aldebaran, the brightest star in Taurus, to- 
gether with Capella and Algol, form an isosceles and nearly 
equilateral triangle, Aldebaran being at the vertex far- 
thest from the pole. Aldebaran is a red star, and with four 
other, but smaller onesj it forms a letter V with its open- 
ing turned towards Capella. This V-shaped cluster is 



38 ASTROKOMY. 

called the Hyades. If the bottom of the V is joined with 
a fourth magnitude star called X Tauri, the V is converted 
into a Y. A smaller and more compact cluster, called the 
Pleiades, 15° northwest of the Hyades, is a prominent ob- 
ject. The stars j3 and £ Tauri, which form the tips of the 
bull's horns, are easily found by the aid of Map III. 

The Ram and the Fishes. A line from e Cassiopeiae 
to y Andromedse when prolonged passes through a Areitis 
and a Piscium, the four stars dividing the line into nearly 
equal parts. The star (3 Arietis' lies about 5° southwest 
of a Arietis, and is a trifle fainter than that star. The 
other stars of these constellations are unimportant, but may 
be traced by means of Map II. 

The "Whale. If the stem of the Y, described in 
speaking of the Hyades, is prolonged it will pass through a 
Oeti, which lies at the vertex of an isosceles triangle, whose 
base is the line joining the Hyades and the Pleiades. About 
one-third of the way from a Ceti to a Piscium we find the 
star y Oeti, and at about 10° southwest of y Ceti is the 
noted variable star called Mira. The other principal stars 
can be found by the aid of Map II. 

The Twins. If a line is drawn from a Persei to a point 
midway between a and (3 Aurigae and then prolonged an equal 
distance it goes to two bright stars in Gemini. The north- 
ernmost of them is named Castor and the southernmost 
Pollux. Both Castor and Pollux are bright stars of the 
second magnitude, and each marks the head of one of the 
twins. The general direction of the body of each of the 
twins is southwest, and is marked by a row of stars. These 
rows which mark the bodies of the twins form a well 
marked and conspicuous rectangle whose breadth is about 
5° and whose length is more than 20°. 

Orion. This is the most magnificent of all the constella- 
tions. It comes to the meridian about 9 o'clock on the 
1st of February, being about 25° southeast of the Hyades. 
It is marked by four brilliant stars which form a trapezoid, 



OF THE STARS. 39 

whose greatest diagonal is nearly 20° in length. The stars 
at the extremities of this diagonal, called Betelgeux and 
Rigel, are both of the first magnitude, and the line joining 
them is nearly bisected by a line of three stars of the third 
magnitude, which form what is called the belt of Orion. 
The extreme stars of the belt are 3° apart, and the middle 
one bisects this distance. Just below them is a line of small 
stars running north and south which form the Sword of 
Orion. The belt points to Aldebaran on the northwest and 
to Sirius on the southeast. 

The Great Dog. The star Sirius, which is the princi- 
pal star of Canis Major, and the most brilliant one in the 
heavens, lies as has been said in the prolongation of the 
belt of Orion to the southeast ; it also lies in the prolonga- 
tion of a line from (5 to k Ononis. This star, which cannot 
be mistaken for any other, enables us to trace out the con- 
stellation to which it belongs. 

The Little Dog. The principal star in Canis Minor is 
called Procyon. It lies to the eastward of Betelgeux, and 
is at one vertex of a nearly equilateral triangle whose other 
vertices are Betelgeux and Sirius. 

The Lion and the Crab. Regulus, the principal star 
in the Lion, is at the eastern vertex of an isosceles triangle, 
whose base is formed by joining Procyon and Pollux. The 
equal sides of this triangle are about 35° in length. The 
triangle just described includes the principal stars of the 
constellation Cancer. Regulus is very near the line formed 
by prolonging the line from a to j3 of the Great Bear. The 
star rj Leonis is about 5° due north of Regulus and, taking the 
line joining them as a handle, the stars y, £ \i, and e form the 
blade of a sickle, whose cutting edge is turned to the west. 
The bright star (3 can easily be found by referring it to the 
stars in the Sickle. 

Hydra. The principal star of this constellation is called 
Cor Hydrae. It lies south of a line joining Regulus and 
Procyon, and is so placed as to form with them a nearly 
equilateral triangle. 



40 



ASTROtfOMY. 



Bootes. If the line from £ to 77 Ursae Majoris is pro- 
longed and slightly curved away from the pole, it will go 
to Arcturus the principal star in Bootes. Arcturus is a star of 
the first magnitude, and is easily recognized. The other 
principal stars can be found by the aid of Maps I. and IV. 

Virgo and Libra. The principal star of Virgo, called 
Spica, is of the first magnitude and about 30° southward of 




Fig. 14. Map IV., 9 p. m., June 1st. 



Arcturus. The other important stars of this constellation 
lie to the north and west of Spica, and are easily traced. 
The four principal stars of Libra form a small quadrilateral, 
whose longest diagonal lies north and south. The upper 
star in the quadrilateral is about 20° nearly west of Spica. 
The Crown, Ophiuchus, the Serpent, and Her- 



OF THE STARS. 41 

Cules. The line from e to £ of the Great Bear if pro- 
longed about 35^ goes to the Crown, and if prolonged 
about 10° further it goes to the head of the Serpent, 
which is marked by the four stars (3, y, «;, and n Serpentis. 
The constellation of the Crown is easily recognized, as it 
consists chiefly of a number of stars very close together, and 
arranged in an arc of a circle whose cou cavity is turned 




Fig. 15. Map V., 9 o'clock p. ar., September 1st. 

towards the north pole. Ophiuchus, or the serpent bearer, 
is represented with his head at the star marked a and with 
his feet on Scorpio, and holding in his grasp a huge ser- 
pent whose general direction is shown on maps V. and IV. 
A line from y to e of the Great Bear when prolonged passes 
through a quadrilateral formed by the stars e, n, £, and n, 



42 ASTHOtfOMY. 

in what is called the girdle of Hercules. Hercules is 
represented as standing with his head at a, his girdle as 
just explained, and his feet reaching nearly to the Dragon. 

The Lyre, the Swan, and the Eagle. The star 
Vega, which is the principal star in the Lyre, and which is 
the brightest star in the northern hemisphere is at the ver- 
tex of a large and nearly right-angled triangle, whose hy- 
pothenuse is a line joining Arcturus and Polaris. It cannot 
be mistaken for any other star. Two small stars towards 
the west and very near Vega form with it a small equi- 
lateral triangle. The upper one is e, a remarkable double 
star. Below and to the eastward are two other stars called 
and y, between which there is a remarkable ring nebula. 
The swan is to the east of Lyra, and its four principal stars 
form a very distinct cross whose length is along the milky 
way. The body of the cross is formed by the stars a, y, 
and (3, and it is completed by the stars 6 and e, which are 
nearly in a line through y. Altair, the principal star in the 
Eagle, is at the southern vertex of an isosceles triangle, 
whose base is formed by a line joining Vega and y Cygni. 
Two small stars, one above and one below Altair, at dis- 
tances of 2° and 3°, form with it an arc slightly curved 
toward the west. 

Pegasus, the Dolphin, and the Waterman. The 
three principal stars of Pegasus, namely a, /3, and y, with 
the star a Andromedae, form a square called the great 
square of Pegasus, whose sides are about 15° in length 
as shown in Map I. The four principal stars of the Dol- 
phin form a beautiful lozenge, which is nearly south of a 
Cygni. It is also on the prolongation of the line from a 
Andromedae to Pegasi. If that diagonal of the great 
square of Pegasus which passes through a Pegasi is pro- 
longed a distance equal to its own length, it will go to a 
Aquarii. To the eastward of a are four stars forming a 
letter Y with its opening turned toward y Pegasi. 

The Scorpion. The line from Eegulus to Spica, when 



Of THE STARS. 43 

prolonged to a distance nearly equal to that between the 
stars named, goes to Antares the principal star in the Scor- 
pion. This is a red star of the first magnitude, and cannot 
easily be mistaken for any other star. Antares is the 
middle one of three stars, forming an arc whose concavity 
is toward the south. At right angles with this, and to the 
westward, is a second arc of three stars, having its concavity 
toward the star a Scorpii. If we imagine this to be the bow 
of a kite, the remaining stars commencing with a form the 
tail, as shown in Map V. 

When the student has become familiar with the leading 
stars of the heavens he can trace out the minor ones by the 
aid of more detailed maps, such as are to be found in Proc- 
tor's Star Atlas. 

The Milky Way. 

35. The Milky "Way, or the Galaxy, as it is often 
called, is a luminous belt, or zone, extending entirely 
around the heavens. It is not everywhere of uniform 
width, is somewhat irregular in its boundary, and it often 
presents deviations, branches, and gaps; on the whole, 
however, its middle line does not differ materially from a 
great circle of the sphere, its inclination to the equinoctial 
being about 63°. It comes nearest to the north pole in the 
constellation Cassiopeia, and to the south pole in the neigh- 
borhood, of the Southern Cross. It is seen most favorably 
during the early evening in the month of September, at 
which time it presents the appearance of a magnificent arch, 
passing through the zenith and running from northeast to 
southwest. 

The telescope shows that this remarkable belt is made up 
of a countless multitude of stars, so far distant from us as to 
be invisible to the naked eye. and so close together as to 
give it the appearance of an almost uniformly luminous 
cloud. It has been estimated that the milky way contains 



44 ASTROKOMY. 

more than 20,000,000 of stars that can be seen with the 
largest telescopes. 

Double and Multiple Stars. 

36. Many stars that seem single to the naked eye, or with 
small telescopes, are in reality double, that is, when viewed 
with more powerful telescopes they are seen to consist of a 
pair of stars, separated from each other by only a few seconds 
of arc. When very powerful telescopes are directed to such 
stars, they are sometimes found to consist of three, four, 
and even more than four components, closely grouped to- 
gether ; such groups are called respectively triple, quadru- 
ple, and multiple stars. 

Herschel limits the class of double stars to those whose 
components are less than 32" apart. The whole number of 
double stars within this limit, so far as known, is more than 
6000. The components of some of these can be seen as 
separate stars with telescopes of moderate power, others re- 
quire for their separation instruments of the highest degree 
of excellence. The stars Castor, [3 Scorpionis, £ Ursae Majo- 
ris, and y Leonis are familiar examples of double stars that 
are easily separated ; Sirius is a double star that can only be 
separated by a powerful telescope. 

The components of a double star may happen to lie in 
nearly the same direction from the observer, and yet be so 
far apart as to have no appreciable physical connection ; 
such stars are said to be optically double. Again, the 
components of a double star may revolve around their com- 
mon centre of gravity in regular orbits ; these stars, which 
are said to be physically connected, are called binary stars, 
to distinguish them from those that are optically double. It 
is highly probable that a great majority of double stars be- 
long to the binary class. 

The star e Lyrae is a striking example of a double binary. 
With a small telescope this star is seen as a widely separated 



OF THE STARS. 45 

but simple double ; wHh a more powerful instrument each 
component is seen to be double. Observation shows that 
the two pairs revolve around their common centre of 
inertia, in an immensely long period, while each of the pairs 
revolves about its own centre of inertia in a very much 
shorter period. 

The star Orionis, which is situated in the midst of a 
great nebulae, presents the appearance of four brilliant stars, 
forming a trapezium whose longest diagonal is about 21" ; 
these are accompanied by two exceedingly minute stars, the 
whole forming a sextuple star, or a multiple star of six com- 
ponents. This group forms a test object for telescopes of 
from 4 to 5 inches aperture. 

Clusters and Nebulae. 

37. In many parts of the heavens great numbers of stars 
are crowded together in masses that are called clusters. 
The Pleiades afford an example of this kind of aggregation; 
in this cluster no more than 
six or seven stars are usually 
visible to the naked eye, but 
when viewed with a telescope 
of moderate power the num- 
ber is increased to sixty or 
seventy. The cluster in Can- 
cer called Praesepe, and the 
cluster in Perseus, are barely 
visible with the naked eye, 
but when viewed with a tele- 
scope they are Shown to COn- Fig. 16. Cluster in Perseus. 

tain hundreds of closely com- 
pacted stars. The telescopic appearauce of the latter is 
shown in Fig. 16. It is on a line from 6 Cassiopeia to 
a Persei at about one-third of the distance from the former. 
The globular cluster in Hercules is another example of an 




ASTRONOMY. 



object which is barely discernible with the naked eye, but 
which is shown in the telescope as a grand assemblage of 
glittering stars. Its telescopic appearance is shown in Fig. 
17 




Fig. 17. Cluster in Hercules. 

In some regions of the heavens the stars, without being 
grouped in regular clusters, are so closely compacted that 
for every star visible to the naked eye there are hundreds 
that are only discernible. with the telescope. Fig. 18 gives 
a telescopic view of a small portion of the constellation 
Gemini, within which there are no more than six or seven 
stars that can be seen with the naked eye. 

The term nebula has been used to designate any of those 
cloud-like patches of faintly luminous matter, of which thou- 
sands are seen by the telescope to be scattered over the dark 
background of the heavens. 

It has been shown by the spectroscope that some of these 



OF THE STAKS. 47 

objects are extended masses of incandescent gases or vapors ; 
these are the true nebulae. 

It is difficult to draw a line of division between clusters 
of stars and nebulae, for many objects that appear to be 




Fig. 18. Star map of a small area in the constellation Gemini. 

nebulae when seen with small telescopes are found to be 
clusters of stars when viewed with instruments of higher 
power. For this reason it has been found convenient to call 
all of these objects nebulae, and then to designate the two 
classes as resolvable and irresolvable. 

Nearly all of the nebulae are exceedingly irregular in 
form ; a few, however, are so nearly regular in shape as to 



48 ASTRONOMY. 

admit of a species of classification. The most noteworthy 
of these classes are the following ; 

1°. The annular nebulae. These are shaped like a 
ring, which may be either circular or elliptical. Only four 
such nebulae are known ; the most remarkable of these is 
situated between the stars (3 and y in the constellation Lyra, 
and may be seen with a telescope of moderate power. The 
nebulous ring is of an elliptical form, and its interior seems 
to be filled with a faintly luminous matter, so that the en- 
tire nebula appears like a tenuous veil stretched on a hoop. 

2°. The elliptical nebulae. These have an elongated 
form, approaching to that of an ellipse. The best example 
of this class is the great nebula of Andromeda. It is faintly 
visible to the naked eye ; when viewed with a small tele- 
scope, its form, is that of an extremely elongated ellipse; 
but under higher powers, its boundaries are greatly ex- 
tended, it loses much of its elliptical form, and presents 
two remarkable black streaks or rifts extending from end 
to end. 

3°. The planetary nebulae. These are nearly circular 
in shape, resembling somewhat the disks of the planets. 
About twenty nebulae of this class are known, some of 
which are double. 

4°. Spiral nebulae. These are but few in number, 
and for the most part can only be seen with telescopes of 
the highest excellence. They appear to be made up of 
irregular spiral bands which spring from a central nucleus 
or eye. The nebula known as 51 Messier, situated in the 
constellation Canes Venatici, is now ranked with the spiral 
nebulae. Sir John Herschel says that in an 18-inch reflector 
it presents the appearance of a large globular nebula sur- 
rounded by a ring which is divided, through two-fifths of its 
circumference, into two laminae. Outside of the ring is a 
bright round nebulous mass. In the great 6-foot reflector 
of Lord Rosse, the principal centre of condensation is seen 
to be the origin of a great number of spiral whorls, the 



OF THE STARS. 



49 



denser portions of which correspond to the ring. These 
curious whorls extend out as far as the secondary centre, 
which also seems to be the origin of a minor set of spiral 
tongues. 

This nebula affords an example of the different appearances pre- 
sented by the same object under different degrees of magnifying 
power. 

Among the more irregular nebulae some are named from 
their apparent form. Of these we may note the crab nebula 




Fig. 19. The Crab Nebula. 



in the constellation Taurus, of which a drawing is given in 
Fig. 19. In ordinary telescopes it has an elliptical outline, 
but in Lord Eosse's telescope "it is transformed into a 
closely crowded cluster, with branches streaming off from 
the oyal boundary, like claws, so as to give it an appearance 
that in a measure justifies the name by which it is distin- 
guished." 
3 



50 ASTRONOMY. 

Fig. 20 represents the central parts of the great nebula of 
Orion as drawn by Trouvelot. It is the most brilliant and 
also the most complicated in form of all the nebulae which 
are visible in our latitudes. It contains in its brightest part 
a multiple star, Orionis. This star consists of four com- 
ponents, arranged in the form of a trapezium, visible in 
a moderately good telescope. It is supposed by some that 
this nebula is variable, that is, its brilliancy is not always 




Fig. 30. Central part of the Great Nebula in Orion as drawn by Trouvelot. 

the same. Another remarkable nebula surrounds the star 
r\ Argus, in the southern hemisphere. 

Fig. 21 is a drawing made by Sir John Herschel. It 
covers an area of the heavens equal to fi\ T e times that cov- 
ered by the full moon. Sir John Herschel studied it with 
an 18-inch reflector, but was unable to discover any indica- 
tion of its being resolvable into stars. 

Tebulae are not distributed uniformly over the heavens. 



OF THE STARS. 51 

In some regions there are but few, and, again, in other 
regions their number is very great. They are particularly 
numerous in the constellations Leo, Virgo, and Ursa Major. 




Fig. 21. Nebula in Argils. 

As a general rule, they increase in number as we recede 
from the milky way, being most numerous near the poles 
of the great circle which marks the general direction of 
that belt. 

Colors and Varying Brightness of Stars. 

38. The color of a great majority of the stars is white 
like the sun, but there are some stars of a yellowish tint, 
some are orange, and not a few are red. Secchi, who bases 
his statement on the evidence of the spectroscope, says that 
" the tints of the stars called white are for the most part 
blue ; from this color there is a passage by insensible de- 
grees to true white, then to yellow, then to orange red, and 
finally to blood red. Sirius, Vega, Castor, and Eegulus are 



52 ASTKONOMY. 

Uue ; Procyon and Altair, white ; Capella, Pollux, and a 
Ceti, yellow ; Aldebaran, Arcturus, and Betelgeux, orange; 
Arcturus and a Hercules, red ; the blood red stars are 
small." 

The components of double stars are frequently colored, 
and in some instances the colors of the two components are 
complementary, that is, colors whose combination would 
form white. In other cases the components have different, 
but not complementary, colors. The components of // Cas- 
siopeiae are yellow and purple ; those of y Andromedse are 
orange and green ; those of (3 Cygni are yellow and blue ; 
those of e Bootis are orange and green ; and those of a Pis- 
cium are pale green and Uue. 

The stars do not always retain the same degree of bright- 
ness ; in fact, many of them experience a remarkable change 
of brilliancy ; these are called variable stars. Secchi says 
that it is probable that all the stars undergo a greater or 
less change in brilliancy. This change is particularly 
marked in those stars whose colors are orange, red, or yel- 
low. In some cases the change is well marked and periodi- 
cal ; in other cases the change is less distinctly manifest, 
and the periodicity is not established. The star o Ceti, 
commonly called Mira, is one of the most remarkable of the 
variable stars. Newcomb says, " during most of the time 
this star is entirely invisible to the naked eye, but at inter- 
vals of about eleven months it shines forth with the bril- 
liancy of a star of the second or third magnitude. It is, on 
the average, about forty days from the time it first becomes 
visible until it attains its greatest brightness, and it then 
requires about two months to become invisible ; so that it 
comes into sight more rapidly than it fades away." An- 
other noted variable star is called Algol, or (3 Persei. It is 
ordinarily of the second magnitude, and retains this degree 
of brightness for about 2d. 13h., when it begins to decline 
in brilliancy, and at such a rate as to become of the fourth 
magnitude in 3|- hours, and then in about the same time it 



OF THE STARS. 53 

regains its original brightness. The total period of this 
star is 2d. 20h. 48m. 55s. 

A class of stars very closely connected with variables 
comprises those which are called temporary. The most 
remarkable star of this class made its appearance in 1572, 
in the time of Tycho Brahe. It was situated in the constel- 
lation Cassiopeia, where it was visible for nearly seventeen 
months, the greater part of which time it was as brilliant as 
Venus ; it finally disappeared after passing from white to 
yellow and then to red. In 1670 a star appeared in the 
constellation of the Swan, which remained visible for two 
years. In 1848 Hind saw a star in Ophiuchus which sud- 
denly became of the fourth magnitude, and is now visible 
as a star of the eleventh magnitude. In 1866 a star in the 
northern crown blazed up to the second magnitude, having 
previously been of the eighth magnitude, and gradually 
subsided to its original brilliancy. It is remarkable that 
the spectrum of this star showed the bright lines of incan- 
descent hydrogen, a fact which gave rise to the theory that 
the increase in brilliancy of this star was due to the sudden 
development of an immense volume of this gas. 



Aspects of the Heavens. 

39. The celestial sphere presents different aspects to 
observers in different latitudes, that is, the diurnal circles 
are differently situated with respect to the horizon. 

First Aspect. — The right sphere. At the equator the 
horizon of the observer coincides with an hour circle, and 
consequently in the course of a sidereal day it sweeps over 
the entire heavens. The diurnal circles are all perpendicular 
to the horizon, and are bisected by it ; hence, all the heavenly 
bodies rise and set in lines perpendicular to the horizon, 
and are as long above the horizon as they are below it. 
A body on the equinoctial rises due east, culminates at 
the zenith, and sets due west. A body that is not on the 



54 



ASTRONOMY. 



equinoctial rises, culminates, and sets at points whose dis- 
tances from the east point of the horizon, the zenith, and 
the west point of the horizon, are respectively equal to the 
declination of the body. 

On account of the obliquity of the ecliptic, the sun is 
sometimes on the north side and sometimes on the south 
side of the equinoctial. At either equinox the sun culmi- 
nates at the zenith ; from the vernal to the autumnal equinox 
it culminates to the north of the zenith, reaching its northern 
limit at the summer solstice when it culminates 23° 27' 
north of the zenith; from the autumnal to the vernal 
equinox it culminates to the south of the zenith, reaching its 
southern limit at the winter solstice, when it culminates 
23° 27' south of the zenith. The days and nights are equal 
throughout the year. 



Explanation. Fig. 22 shows the right 
sphere projected on the plane of the 
solstitial colure, the equinoxes being in 
the horizon; HH 7 is the projection of 
the horizon ; ZZ' is the projection of 
the prime vertical ; and KK' is the pro- 
jection of the ecliptic ; KB is the projec- 
tion of the sun's diurnal circle at the 
summer solstice ; and CK 7 is the projec- 
tion of its diurnal circle at the winter 
solstice. 



Second Aspect. — The par- 
allel sphere. At either 
pole, say the north pole, the 
horizon of the observer coin- 
cides with the equator, and always remains fixed in position. 
The diurnal circles are all parallel to the equator. The 
fixed stars neither rise nor set, but circle around, remaining 
always at distances from the horizon equal to their respect- 
ive declinations. Those north of the equinoctial are always 
above the horizon, and those south of the equinoctial are 
always below the horizon. 

The sun is in the horizon, or rises, at the vernal equinox; 




Fig. 22. The Right Sphere. 



OP THE STARS. 



55 



it then ascends slowly till the summer solstice, when its dis- 
tance above the horizon is 23° 27' ; from that time it de- 



till the time of the autumnal equinox, when it is 
again in the horizon, or sets. From this time till the next 
vernal equinox it remains below the horizon. Hence, we 
say that the days and nights at the pole are six months in 
length. 




Fig. 23. The Parallel Sphere. 



Explanation. The figure represents the 
parallel sphere projected on the plane of 
the equinoctial ; EAQV is the equinoctial ; 
V is the vernal equinox ; A is the autumnal 
equinox ; and VA is the line of equinoxes ; 
VSA is the projection of that half of the 
ecliptic which lies north of the equinoctial, 
S being the projection of the summer sol- 
stice; SBS' is the projection of the sun's 
diurnal circle on the day of the summer 
solstice. 



Third Aspect. — The ob- 
lique sphere. To an ob- 
server at any point between 
the equator and either pole, 

say at a point between the equator and the north pole, 
the horizon is oblique to the axis of the earth, the angle of 
inclination being equal to the latitude of the place. The 
diurnal circles are all oblique to the horizon, the angle of 
inclination counted from the south point being equal to 
the complement of the latitude, that is, to the co-latitude of 
the place ; all of these circles except the equinoctial itself 
are unequally divided by the horizon. For bodies south of 
the equinoctial the part above the horizon is less than the 
part below, and for bodies north of the equinoctial the part 
above the horizon is greater than the part below ; hence, a 
body whose declination is south is longer below than it is 
above the horizon, and a body whose declination is north is 
longer above the horizon than it is below. 

A circle described about the north pole, with a spherical 



56 



ASTEOHOMY. 



radius equal to the latitude of the place, is called the circle 
of perpetual apparition, and a circle about the south 
pole with an equal radius is called the circle of per- 
petual occultation. 

All bodies north of the circle of perpetual apparition are 
always above the horizon, and all bodies south of the circle 
of perpetual occultation are always below the horizon, that 
is, they are perpetually invisible. 

If a body's declination is less than the latitude of the 
place, it culminates south of the zenith ; if its declination 
is equal to the latitude, it culminates at the zenith ; and if 
its declination is greater than the latitude it culminates 
north of the zenith. 




Fig. 24. The Oblique Sphere. 



Explanation. The figure represents 
the projection of the oblique sphere on 
the plane of the solstitial colure, the 
equinoxes being in the horizon ; PP' is 
the axis of the heavens ; Z is the zenith 
of the place (supposed to be in north lati- 
tude) ; HH' is the projection of the hori- 
zon ; Q,Q/ is the projection of the equi- 
noctial ; KK' is the projection of the 
ecliptic ; K being the summer and K' the 
winter solstice ; KB is the projection of 
the sun's diurnal circle on the 21st of 
June ; AK' is the projection of the sun's 
diurnal circle on the 21st of December ; 
HZ is the projection of the circle of per 
petual apparition ; and H'M is the pro- 
jection of the circle of perpetual occulta- 
tion. The latitude of the place is equal 
to the angle Q'EZ, or to the angle HEP. 



When the sun is at either equinox it rises due east, cul- 
minates at a point whose distance south of the zenith is 
equal to the latitude of the place, and sets due west. . At 
these times the days and nights are equal. When the sun 
is south of the equinoctial, that is, from the autumnal to 
the vernal equinox, it rises to the south of east, and sets to 
the south of west, the days being shorter than the nights. 
When the sun is north of the equinoctial, that is, from the 



OF THE STARS. 57 

vernal to the autumnal equinox, it rises to the north of east 
and sets to the north of west, the days being longer than the 
nights. When the sun is at the winter solstice the days are 
shortest and the nights longest; when the sun is at the 
summer solstice the days are longest and the nights are 
shortest. 

From what has been said above, we see that the difference 
between the lengths of the days and nights depends upon 
the latitude of the place and the position of the sun in its 
apparent path amongst the stars. 

Additional Definitions. 

40. The diurnal circles of the sun, when at the solstices, 
are called Tropics, the northern one being the Tropic of 
Cancer, and the southern one being the Tropic of 
Capricorn. 

The diurnal circles through the poles of the ecliptic are 
called Polar Circles, the northern one being the Arctic 
Circle, and the southern one being the Antarctic Circle. 

Corresponding circles on the surface of the earth are 
called by corresponding names. 

At the tropics the inequality in the lengths of days and 
nights varies from to 2h. 54m. ; between the tropics and 
polar circles it varies from to 24 hours ; and within the 
polar circles it varies from to 6 months. 

Varying Inclination of the Ecliptic to the Horizon. 

41. The ecliptic being oblique to the axis of the heavens, 
its inclination, Avith respect to the horizon, will be variable. 
It makes the greatest angle with the horizon when the ver- 
nal equinox is at the west point of the horizon ; this angle 
is equal to the co-latitude of the place plus the inclination 
of the ecliptic. It makes the least angle with the horizon 
when the vernal equinox is at the east point of the horizon ; 



58 ASTRONOMY. 

this angle is equal to the co-latitude of the place, minus the 
inclination of the ecliptic. 

At a place whose latitude is 40°, the co-latitude is 50°, the greatest 
inclination of the ecliptic to the horizon is 73° 27', and the least incli- 
nation is 26° 33'. The inclination may have any value between these 
limits. 



Proper Motion of the Stars. 

42. The bodies heretofore considered, that is, the stars 
and nebulce, though regarded as fixed, are really in motion, 
but on account of their enormous distances from us and 
from each other their motions are scarcely perceptible ; they 
are indeed so slight that thousands of years would be re- 
quired to produce a change of relative position that would 
be apparent to the naked eye. Of the stars that are found 
to have a proper motion, that is, a motion with respect 
to the other stars, only a few move more than a single 
second of arc in a year, whilst by far the greater number 
move but a few seconds in a century. A part of what is 
usually called the proper motion of the stars is due to the 
motion of the sun, which belongs to the same class of bodies 
as the stars, and which, like them, is undoubtedly moving 
through space, carrying the planets and their satellites 
with it. 

The bodies we are next to consider are much nearer to us than the 
stars, and for this reason their motions are more obvious. 



III. THE SOLAR SYSTEM. 

Bodies that Constitute the Solar System. 

43. We have already seen that the sun appears to have 
a progressive motion from west to east, completing the cir- 
cuit of the heavens in a period that we call a year. 

The moon also has a progressive motion from west to 
east among the stars, advancing at an average rate of a 
little more than 13° a day, completing the circuit of the 
heavens in about 27^ days. In her eastward motion she 
gains on the sun a little more than 12° per day, so that if 
the two bodies have the same right ascension, at any time, 
their right ascensions will again be the same after a period 
of about 29-| days, which period is called a lunar month. 

Besides the sun and moon, whose eastward motion is pro- 
gressive and comparatively regular, there are other bodies 
that move irregularly among the stars, sometimes ad- 
vancing, that is, moving from ivest to east, and sometimes 
retrograding, that is, moving from east to west. The arcs 
through which they advance are always greater than those 
through which they retrograde, so that they ultimately 
complete the entire circuit of the heavens, which they do 
in periods ranging from a little less than 3 months up to 
more than 164 years. The principal bodies of this class are 
called planets, and the minor ones planetoids. 

Many of the planets are accompanied by secondary bodies 
that revolve around them as centres in the same way that 
they themselves revolve around the sun. These bodies are 
called satellites ; thus, the moon is a satellite of the earth. 

If to these we add comets, which occasionally appear in 
the heavens and meteoric streams, which seem to be 



60 A3TROHOMY. 

closely allied to comets, we have all the bodies whose mo- 
tions can readily be observed. 

The bodies above enumerated, including our earth, which 
is a planet, constitute a closely connected group called the 
solar system. 

Plan of the Solar System. 

44. 1°. The sun is the central body of the system. As 
already stated, the sun belongs to the same class of bodies 
as the stars ; like them it has its own proper motion through 
space, but this motion is so small that it may be disregarded 
in a general view of the heavens ; we may therefore regard 
its position as fixed. 

2°. The planets, of which eight are now known, revolve 
around the sun from west to east in orbits that are nearly 
circular, and whose planes are but slightly inclined to each 
other. These orbits are really ellipses, each of which has 
one focus at the sun. 

The names of the planets, in the order of their distances 
from the sun, and the signs by which they are designated, 
are as follows: 1st. Mercury, § ; 2d. Venus, $ ; 3d. Earth, 
© ; 4th. Mars, $ ; 5th. Jupiter, U ; 6th. Saturn, h ; 7th. 
Uranus, V or £ ; and 8th. Neptune, f . Mercury and 
Venus, being nearer to the sun than the earth, are called 
inferior planets ; Mars, Jupiter, Saturn, Uranus, and 
Neptune are called superior planets. 

The orbits of the planets are so little inclined to each other that 
they are all included within a cylindrical disk, whose diameter is 
twice the greatest distance of Neptune from the sun, and whose 
height, or thickness, is considerably less than ^ of its diameter. 
This disk, whose bases are symmetrically situated with respect to the 
ecliptic, is thinner in proportion to its diameter than the thinnest of our 
government coins, and it has been found by observation that it always 
retains a fixed position with respect to the stars. Hence, for the ordi- 
nary purposes of description we may regard the planets as revolving 1 
in orbits which lie in the plane of the ecliptic. 



THE SOLAR SYSTEM. 61 

3°. The planetoids, of which more than 230 are now 
known, revolve around the sun from west to east in ellipti- 
cal orbits, each of which has one of its foci at the sun. 

The planetoids differ from the planets in several partic- 
ulars, the most noticeable of which are the following : 
1st, they are vastly smaller than the smallest planet ; 
2dly, their orbits are much more excentric ; and 3dly, 
the planes of their orbits are generally much more in- 
clined to the ecliptic. 

4°. The satellites, of which 20 are now known, revolve 
around their primaries, that is, around the planets to which 
they belong, and at the same time they accompany these 
planets in their journey around the sun. 

Of the known satellites, the earth has 1, Mars 2, Jupiter 
4, Saturn 8, Uranus 4, and Neptune 1. Of these, the first 
15 revolve around their primaries in the same direction that 
the planets revolve around the sun, that is, their motions 
are direct ; the remaining 5 revolve around their primaries 
in an opposite direction, that is, their motions are retro- 
grade. 

5°. The comets which appear from time to time, re- 
volve around the sun in orbits that are ahvays more excen- 
tric, and frequently more inclined to the ecliptic, than those 
of the planetoids. In some cases their motions are direct, 
and in some cases they are retrograde. 

The orbit of a comet may be an ellipse, a parabola, or an 
hyperbola, but it always has one of its foci at the sun. 
Those comets which are permanent members of our system 
move in extremely elongated ellipses. 

6°. The meteoric streams, which consist of myriads of 
minute bodies scattered over immense spaces, revolve around 
the sun in orbits that resemble those of the permanent 
comets of our system, with some of which they appear to 
be closely connected. 



62 ASTBOKOMY. 



Definitions and Principles. 

45. Because the orbits of the planets are ellipses, each 
having one of its foci at the sun, the distance of any planet 
from the sun is continually changing ; when nearest the 
sun it is said to be in perihelion, and when farthest from 
the sun it is said to be in aphelion. 

The perihelion and the aphelion points of any orbit are 
the vertices of its transverse, or major axis ; the former 
is sometimes called the lower, and the latter the upper 
apsis, and in this case the transverse axis itself is called 
the line of apsides. 

A line from either focus of an ellipse to any point of the 
curve is called a radius-vector ; it is shown in analytical 
geometry that the mean or average value of all the radii - 
vectores that can be drawn from either focus of an ellipse to 
the curve, is equal to the semitransverse axis of that ellipse. 
Hence, the mean distance of any planet from the sun 
is equal to half the sum of its perihelion and aphelion dis- 
tances. 

The excentricity of an ellipse is the distance from its 
centre to either focus divided by the semitransverse axis, or 
what is the same thing, it is equal to the distance betiveen 
its foci divided by its transverse axis. Hence, the excen- 
tricity of the orbit of a planet is equal to the difference be- 
tiveen its aphelion and perihelion distances, divided by the 
sum of those distances. 

Dimensions of the Planetary Orbits. 

46. The mean distance of the earth from the sun, in 
terms of which the mean distances of all the other planets 
are expressed, is itself dependent on the solar parallax, 
that is, on the semi-angle subtended by the earth as seen 
from the sun. The determination of this angle has occu- 
pied much of the attention of astronomers for a long period 



THE SOLAR SYSTEM. 



63 



of time, and Prof. Newcomb, in summing up the results 
deduced from all the different methods that have been used, 
but not including those of the various expeditions that were 
sent out to observe the transits of Venus in 1874 and 1882, 
says that its value is probably between 8".82 and 8". 86. If 
we take the mean of them, or 8". 84, as the true value of 

MARS 




Fig. 25. Diagram of the orbits of the four interior planets. 

Explanation. The scale of the diagram is one inch to 92£ millions of miles. 
The sun being at S, the direction of V-E from S, is that of the vernal equinox ; and 
the perihelion point of each orbit is shown by the place of the sign, that designates 
the corresponding planet. 



the parallax, the mean distance of the earth from the sun 
is nearly 92 \ millions of miles. Assuming this as the cor- 
rect distance of the earth from the sun, the mean distances 



64 



ASTRONOMY. 



of all the planets, to the nearest quarter of a million of miles, 
are given in Table I. The same table gives the excentricitj 
of each of the planetary orbits with the corresponding 
perihelion and aphelion distances, to the nearest quarter of 
a million of miles. 

NEPTUNE 




Fig. 26. Diagram of the orbits of the four exterior planets on a smaller scale. 

Explanation. The scale of the diagram is ^ of an inch to 92| millions of 
miles. In order that it may be compared with the preceding diagram, it must be 
enlarged 20 times in all directions ; S is the place of the sun ; the direction from 
S to V-E is that of the vernal equinox : and the perihelion points of the different 
orbits are denoted by the places of the signs that designate the corresponding 
planets. 



The orbits of the planetoids are situated between those 
of Mars and Jupiter, the mean distances of the planetoids 
being greater than 200 millions of miles, and less than 330 



THE SOLAR SYSTEM. 



65 



millions of miles. The excentricities of the orbits of the 
planetoids range from .0229 up to .3468, the average value 
being about 2 \ times as great as that of the planetary orbits. 

TABLE I. 



Name of 
Planet. 


Mean distance 

in millions of 

miles. 


Excentricity 
of orbit. 


Perihelion 
distance. 


Aphelion 
distance. 


Mercury 

Venus 

Earth 

Mars 

Jupiter 

Saturn 

Uranus 

Neptune .... 


35f 

66| 
92i 
141 

480 

881 
1771 

2775 


.2056 
.0068 
.0168 
.0933 
.0483 
.0560 
.0464 
.0090 


28i 

661 

91 

128 

457 

832 

1689 

2750 


43 

67i 

94 

154 

503 

930 

1853 

2800 



Note. — Prof. Young, in his recent work on the sun, is inclined to 
adopt 8". 8 as the most probable value of the solar parallax. This 
would make the earth's mean distance from the sun nearly one-half of 
one 'per cent, greater than that given in Table I., and would require 
a proportional change in all the other distances in the table. It 
would also require a corresponding change in the values of the quan- 
tities given in Table II. 



Distribution of Volumes and Masses. 

47. It has been shown from geodesic surveys that the 
earth has the shape of an oblate spheroid, that is, of a 
sphere flattened at the poles, its equatorial diameter being 
about 7925.6 miles and its polar diameter about 7899.2 
miles. It has been found by astronomical observation that 
Mars, Jupiter, and Saturn are also oblate spheroids, but 
evidences of flattening have not been discovered in any of 
the remaining planets. The diameter of the sun and the 
greatest and least diameters of each of the planets are given 
in Table II.; that table also contains the volumes of these 
bodies in terms of the earth's volume, which is taken as a 
unit. This table has been computed on the supposition 
that the solar parallax is 8". 84; should any correction be 



66 



ASTRONOMY. 



made in this element, it would require a corresponding cor- 
rection in the table. The relative diameters of the planets 
are shown in Fig. 27. 



The masses of the planets, 
by which we mean the 
quantities of matter they 
contain, are the same as 
those given by Prof. New- 
comb, except that the earth 
has been taken as a unit in- 
stead of the sun. He says 
that the masses of many of 
the planets are still very un- 
certain, for the reason that 
exact observations have not 
as yet been continued long 
enough to admit of their 
satisfactory determination. 
He also says that the diame- 
ters are uncertain in many 
cases, but especially in those 
of the outer planets, Uranus 
and Neptune. 




Fig. 27. 



Diagram showing the relative 
sizes of the planets. 



TABLE II. 



Body. 


Diameter in miles. 


Volume 
Earth=l. 


Mass 
Earth=l. 


Greatest. 


Least. 


Sun 


860,000 

2,990 

7,660 

7,925 

4,220 

87,770 

72,980 

31,690 

34,800 


860,000 

2,990 

7,660 

7,899 

4,196 

82,570 

65,580 

31,690 

34,800 


1,281,900 
.054 
.9058 

1 

.1506 

1,282 

704 

64 

85 


326,800 
.065 
.769 
1 
.11 
312 
93 
14 
17 


Mercury 

Venus 


Earth 

Mars 


Jupiter 


Saturn 


Uranus 


Neptune 



THE SOLAR SYSTEM. 67 

It will be seen from the table that the volume of the sun is more 
than 600 times the aggregate of the volumes of all the planets, and 
that the mass of the sun is more than 700 times the combined masses 
of all the planets. 

Popular Illustrations. 

48. To illustrate the relative magnitudes and distances 
of the sun and planets, take an ordinary 36-inch globe to 
represent the sun and pass a horizontal plane through its 
centre to represent the ecliptic in which we suppose all the 
planets to move. Then, on the same scale, Mercury will be 
represented by a globule whose diameter is -J- of an inch, 
and its orbit will be represented by a circle whose diameter 
is 250 feet ; the diameters of Venu^ and the Earth will each 
be about -j- of an inch, the orbit of the former having a 
diameter of 468 feet, and that of the latter a diameter of 
646 feet ; Mars will be represented by a globule ^ of an 
inch in diameter, and its orbit will have a diameter of 984 
feet; Jupiter, the " giant planet" of the system, will have 
a diameter of 3-J- inches^and its orbit will be 3,360 feet 
across ; Saturn will be represented by a ball 3 inches in 
diameter, and its orbit will have a diameter of 6,160 
feet ; Uranus and Neptune will be represented by balls 
whose respective diameters are 1^ and 1|- inches, the for- 
mer moving in a circle whose diameter is 13,390 feet, and 
the latter in one whose diameter is 19,380 feet, or more 
than 3^ miles. 

Some idea maybe formed of the enormous distance from 
the sun to Neptune if we recollect that a railway train 
whose speed is 38 miles an hour would require three years 
to accomplish a million of wiles. A body traveling at 
this rate would require more than 8,000 years to traverse 
the distance from the sun to Neptune, and more than 
50,000 years to accomplish the entire circuit passed over 
by Neptune in his journey around the sun. And yet 
these distances, which are almost inconceivably great, 



68 ASTRONOMY. 

dwindle into insignificance in comparison with the still 
greater distances that separate the sun from the nearest 
of the fixed stars. 



Definitions and Principles. 

49. In determining the relative positions of the bodies 
belonging to the solar system, it is often convenient to re- 
fer them to the ecliptic instead of to the equinoctial. In 
this case the elements of reference are called celestial lati- 
tude and celestial longitude. 

The celestial latitude of a body is its angular dis- 
tance from the ecliptic ; it is measured on the arc of a 
great circle passing through the body and perpendicular 
to the ecliptic. It is positive when the body is north of 
the ecliptic, and negative when the body is south of the 
ecliptic. 

The celestial longitude of a body is the angular dis- 
tance from the vernal equinox to the foot of an arc passing 
through the body and perpendicular to the ecliptic. It is 
reckoned from the vernal equinox around to the east 
through 360°, and is always positive. 

Sometimes the place of a body is referred to the centre of 
the earth, and sometimes to the centre of the sun ; in the 
former case it is said to be geocentric, and in the latter it 
is heliocentric. Thus, the geocentric longitude of a heav- 
enly body is its longitude as seen from the centre of the 
earth, and its heliocentric longitude is its longitude as seen 
from the centre of the sun. 

When the terms latitude and longitude are used without 
qualification they are to be understood as meaning geocen- 
tric latitude and longitude. Latitudes and longitudes of 
the heavenly bodies cannot be found by direct observation, 
but when we know the obliquity of the ecliptic, together 
with the right ascension and declination of a body, we can 
compute its latitude and longitude, 



THE SOLAR SYSTEM. 69 



Explanation. V is the vernal equinox ; 
VR an arc of the equinoctial ; VD an arc of 
the ecliptic ; P the place of a body ; QP, per- 
pendicular to VR, is the declination, and VQ 
the right ascension of P ; CP, perpendicular to 
VD, is the latitude, and VC the longitude of P ; 
and PV is an arc of a great circle. 




Fig. 28. 



When we know QV and QP in the 
right-angled triangle VQP, we can find, by the principles of trigonom- 
etry, the angle QVP and the arc VP. In the right-angled triangle 
VPC the angle CVP is equal to the difference between QVP and the 
obliquity RVD, and consequently we cau find CP and VC, the latitude 
and the longitude of P. 

50. Two bodies are in conjunction ( 6 ) when they have 
the same longitude ; they are in opposition ( 8 ) when their 
longitudes differ by 180° ; and they are in quadrature (Q ) 
when their longitudes differ by 90°, or by 270°. 

When two bodies have the same right ascension they are 
said to be in conjunction in right ascension, and when their 
right ascensions differ by 12h. they are said to be in opposi- 
tion in right ascension. 

The terms conjunction and opposition are used in the former sense 
when the places of the bodies are given by longitudes and latitudes, 
and in the latter sense when their places are given by right ascensions 
and declinations. In determining the times of new and full moon it 
is customary to use these terms in the former sense, but in the compu- 
tation of eclipses and occultations it is found to be more convenient to 
use them in the latter sense. 

An inferior planet has two kinds of conjunction with the 
sun : it is in inferior conjunction when it is between 
the earth and the sun, and in superior conjunction when 
the sun is between it and the earth. 

The elongation of a body is its angular distance from the 
sun. The elongation may be reckoned on the great circle 
passing through the body and the sun, but more commonly 
it is reckoned on the ecliptic, in which case it is equal to the 



70 ASTRONOMY. 

difference between the longitude of the body and that of the 
sun. 

A superior planet may have any elongation from 0°, when 
it is in conjunction, up to 180°, when it is in opposition. 
The elongation of Mercury is never greater than about 29°, 
and that of Venus is never more than 48°. When a planet 
is in eastern elongation it sets after the sun and is called 
an evening star; when in western elongation it rises be- 
fore the sun and is called a morning star. 

51. The periodic time of a planet is the time required 
for the planet to make a complete revolution around the 
sun. 

The synodic period of a planet is the interval between 
two successive conjunctions of the planet with the sun, or 
between two successive oppositions of the planet and the 
sun. 

It will be shown hereafter that the periodic .time of a planet can he 
found when we know its synodic period and the periodic time of the 
earth. 

The inclination of the orbit of a planet is the an- 
gle between the plane of the orbit and the plane of the 
ecliptic. 

The nodes of a planet are the points in which the orbit 
of the planet intersects the plane of the ecliptic. The 
ascending node is the point at which the planet passes 
from the south to the north side of the ecliptic, and it is 
often designated by the sign Q ; the descending node is 
the point at which the planet passes from the north to the 
south side of the ecliptic, and it is designated by the 
sign q. 

The line of nodes is the line joining the ascending and 
the descending node ; it is the intersection of the plane of 
the planet's orbit with that of the ecliptic. 



THE SOLAR SYSTEM. 
TABLE III. 



71 





Periodic time. 














Synodic 


Inclina- 


Heliocentric 


Heliocentric 


Body. 






period 


tion of 


Long, of 


Long, of 




In days. 


In 
years. 


in days. 


orbit. 


Perihelion. 


As. node. 


Mercury. . 


87.97 


0.24 


115.9 


7°.00 


75°. 12 ■ 


46 3 .55 


Venus.. . . 


22470 


0.62 


583.9 


3 D .39 


129°.45 


75°.33 


Earth . . 


365.25 


1.00 






100°. 36 


.... 


Mars 


686.98 


1.88 


779.8 


l c .85 


333°. 30 


48 c .40 


Jupiter.. . 


4,332.58 


11.86 


398.8 


1°.31 


11°.92 


98°.94 


Saturn . . . 


10,759.22 


29.46 


378.0 


2°.49 


90 P .07 


112°.35 


Uranus . . . 


30,686.82 


8401 


369.7 


0\77 


170°.6o 


73°.24 


Neptune. . 


60,126.71 


16462 


367.5 


1°.78 


49 c .15 


130°. 12 



Kepler's Laws and the Newtonian Law. 

52. Early in the 17th century Kepler announced three 
laws of planetary motion, which have since been known as 
Kepler's laws. They are as follows : 

T. The orbit of each planet is an ellipse, one focus 
of which is at the sun. 

2°. As the planet revolves around the sun its 
radius-vector sweeps over equal areas in equal 
times. 

3°. The squares of the times of revolution of the 
planets are proportional to the cubes of their mean 
distances from the sun. 

These three laws would be rigorously true if the planets 
were material points, but in consequence of the mutual 
attraction of the planets upon each other the laws require 
slight corrections. These corrections, or rather the changes 
that call for the corrections, are called perturbations. 

Sir Isaac Newton showed that Kepler's laws were simple 
consequences of a more general law. which is known as 
Newton's law of universal gravitation. This law 
may be enunciated as follows : 



72 ASTRONOMY. 

Every particle of matter in the solar system at- 
tracts every other -particle, with a force that varies 
directly as the mass of the attracting particle, and 
inversely as the square of the distance between the 
particles. 

The attraction between two bodies is mutual, that is, each particle in 
one acts upon every particle of the other according to the above law. 
If, therefore, we take the mutual attraction of two units of mass at a 
unit's distance from each other as the unit of attraction, and call it 1, 
the mutual attraction of two bodies whose masses are m and m' at the 
unit's distance will be m x m' , and at the distance d it will be m x m' 
divided by d 2 . Hence, the measure of the mutual attraction of two 
bodies is equal to the product of their masses divided by the square of 
the distance between them. 

It is certain that the Newtonian law extends throughout the solar 
system, and it is extremely probable that it holds good throughout the 
physical universe. 



IV. THE EARTH. 

Astronomical Importance of the Earth. 

53. The Earth is one of the smallest of the planets, but 
from an astronomical point of view it is the most important 
of them all. Its distance from the sun is the primary 
unit in terms of which we measure the dimensions of the 
solar system ; its mass is the unit employed in measuring 
the masses of all the other bodies of the system ; the period 
required for it to revolve on its axis gives us one ulti- 
mate unit of time ; and finally, it is the standpoint from 
which we observe all the phenomena of the heavens. 

These relations seem to indicate that its study should precede that 
of the other bodies of the solar system. 



General Form of the Earth. 

54. By the general form of the earth we mean the form 
that it would present to an observer at a distance so great 
as to render inappreciable the irregularities of hill and dale 
that roughen its surface. That this form is globular may 
be inferred from the following considerations : 

1°. From its appearance as seen from different points. 
Its apparent form is best seen at sea. If we stand on the 
deck of a vessel out of sight of land, or if we ascend to the 
mast-head, the visible part of the ocean seems to be limited 
by the circumference of a circle. In like manner if we view 
the earth from a mountain-top, or from a balloon, its out- 
line always seems circular. Inasmuch as a globe is the only 



74 ASTRONOMY. 

body that appears circular from every point of view, we are 
led to infer that the earth is globular. 

Universal experience shows that the more elevated the point of 
view, the more extended is the visible part of the earth's surface, and 
consequently the more elevated an object is, the greater the distance 
from which it is visible. Thus, at sea an approaching vessel first 
shows the tops of her masts, then her principal sails, and finally her 
hull comes in sight ; also, when a receding vessel has entirely disap- 
peared from the view of an observer on deck, she again becomes visi- 
ble if he ascends to the mast-head. 

2°. From analogy. Observation shows us that all the 
other bodies of the solar system are globular, and we may 
infer from analogy that the earth does not differ from them 
in form. 

3°. From actual measurement. Actual measurement of 
arcs of meridians and circles of latitude show that the earth 
is globular, but not quite spherical. Its real form is that of 
a sphere flattened at the poles, but the flattening is so slight 
that we may, for the purposes of descriptive astronomy, 
regard it as truly spherical. 

Comparative Roughness of the Earth's Surface. 

.55. The loftiest mountain on the surface of the earth 
hardly exceeds 5 miles in height, which is only l6 1 00 of the 
earth's diameter. On a 16-inch globe such a mountain 
would be represented by an elevation of y^ of an inch, 
which is about the thickness of ordinary drawing-paper. 
But the average elevation of even the most mountainous 
countries does not amount to the fifth part of this, so we 
may truly say that the inequalities of hill and valley are 
insignificant in comparison with the entire earth. The 
greatest depths of the ocean are not much more than 5 
miles, and its average depth is very much less than this, so 
that the depth of the ocean is also insignificant in compari- 
son with the diameter of the earth. 



THE EARTH. ?5 

Dimensions of the Earth. 

56. Having ascertained that the earth is globular, an ap- 
proximate value for its diameter may be found as follows : 

A meridian line of suitable length is laid out by the aid 
of a portable transit iustrument and its two ends are marked 
by signals. The length of the line is then determined by 
geodesic survey, and the latitudes of its extreme points are 
found by one of the methods yet to be explained. Assum- 
ing the earth to be an exact sphere and the measured arc to 
lie w r holly on one side of the equator, the difference between 
the latitudes found will be the angle subtended by the arc 
as seen from the centre of the earth. The length of the 
entire circumference, or the length of a single degree, may 
then be found by means of the geometrical principle that 
the length of any arc of a circumference is proportional to 
the angle that it subtends. 

Denoting the length of the measured arc by I, the corresponding 
angle at the centre by n°, and the circumference of the earth by c, we 

have the proportion, n° : I : : 360° : c ; .*. c = x I. 

The diameter is equal to the circum- 
ference divided by it, that is, by 3.1416 ; 
it is found to be a little more than 7,900 
miles. 

Again, if we denote the length of 1° 
of the meridian by d, we have the pro- 
portion n° : I : : 1° : d ; „••. d = —. 



Explanation. AC is the measured arc, I ; 
Q'EA is the latitude of A : and Q'EC is the 
latitude of C Fig 2g 



When the lengths of a degree of the meridian are meas- 
ured in different latitudes it is found that they are longer 
the nearer they are to the pole, from which it is to be in- 
ferred that the meridians become less curved, that is, they 




76 ASTHOKOMY. 

grow flatter as they approach the poles. From a great num- 
ber of arcs measured in different latitudes and on different 
meridians it has been shown that the true form of the earth 
is that of an oblate spheroid, that is, of a volume generated 
by revolving an ellipse around its shorter axis. Prof. Airy 
showed by a process of the higher mathematics that the 
longer axis of this ellipse, or, in other words, the equa- 
torial diameter of the earth, is equal to 7925. 648 miles, 
and that the shorter axis, or the polar diameter of the 
earth, is 7899.17 miles in length. If we define the mean 
diameter of the earth to be the diameter of a sphere whose 
volume is equal to the actual volume of the earth, we can 
easily show that it is equal to 7916.81 miles; hence we say 
in round numbers that the mean diameter of the earth is 
equal to 7917 miles. 

Its Ellipticity and the Equatorial Protuberance. 

57. The ellipticity of an oblate spheroid is measured by 
the difference between its greatest and least diameters divided 
by its greatest diameter. 

The difference between the greatest and least diameters of the earth 

26 478 1 

is 26.478 miles ;• hence its ellipticity is equal to ~ f T OK ,;Tq or to 



7925.648 299.33 

If we imagine a sphere to be described on the polar diame- 
ter of the earth, that portion of the earth which lies without 
the sphere is called the equatorial protuberance. 

The equatorial protuberance is 13.239 miles thick at the equator, 
and grows thinner as it approaches the poles, where its thickness is 0. 
The volume of the equatorial protuberance is about T fg- of the entire 
volume of the earth, although its mass is probably not more than ¥ ^ 
of the entire mass of the earth. 

Probable Cause of the Earth's Spheroidal Form. 

58. The earth's rotation gives rise to a centrifugal force 
in each of its particles whose direction is perpendicular to 



THE EARTH. 77 

the axis and whose intensity is equal to the continued 
product of the mass of the particle, the square of its angu- 
lar velocity, and its distance from the axis. If the cen- 
trifugal force acting on each particle is resolved into two 
components, one in the direction of the vertical through 
the particle and the other perpendicular to it, the former 
will always act to diminish the apparent weight of the par- 
ticle, and the latter will tend to draw it toward the equator. 
The general effect of these two components is to heap up the 
matter of the earth in the neighborhood of the equator, and 
this action must go on till an equilibrium takes place be- 
tween all the forces acting on each particle, (Peck's Ele- 
mentary Mechanics, Art. 128). Now, it has been shown, 
by means of the higher analysis, that the form of equi- 
librium of a plastic body, whose matter is distributed as 
we have reason to suppose is the case in our earth, is that 
of an oblate spheroid whose shape is that which our earth 
has been shown to have. We therefore infer that the earth 
was probably once in aplastic condition, and that its present 
form is due to the combined action of gravity and the cen- 
trifugal forces upon each of its particles. 

This inference is strengthened by the fact that other 
planets are flattened at the poles, and that those which 
revolve more rapidly than the earth are still more flattened 
than it. 

It is to be noted that the amount of flattening of a rota- 
ting mass will depend not only on the rapidity with which 
the body rotates, but also on the relative distribution of its 
matter with respect to density. 

The Torsion Balance. 

59. The torsion balance is a species of horizontal pen- 
dulum used to measure small horizontal forces. It consists 
of a slender rod of homogeneous material terminating in 
two equal metallic balls and suspended at its middle point 



78 ASTRONOMY. 

by a delicate wire. The upper end of the wire is attached 
to a fixed support and the rod is so placed that it can re- 
volve freely in a horizontal plane. 

|") Explanation. A and B in Fig. 30 are spheri- 

cal balls of metal; DC is a suspending fibre or 
wire ; and AB is a horizontal rod of wood or other 
homogeneous substance. 

The wire DC is firmly attached to a fixed ceiling 
atD. 

When this wire is twisted by turn- 
ing the rod in azimuth, its elasticity 
B is called into play, and when the rod 
q P is set free, it is forced back to its 

Fig. so. Torsion balance, original position, which it reaches 
with a living force sufficient to carry 
it as far to the other side ; a force of torsion is thus de- 
veloped in an opposite sense, which causes the pendulum 
again to return, and so on indefinitely. The vibration 
thus set up is in all respects similar to that of an ordinary 
pendulum, and when we know the time of a single vibra- 
tion (which is independent of the length of the arc of 
vibration), it is a simple matter to compute the value of 
the force that must be applied to either ball to turn the 
rod through a unit of angular measure. Again, knowing 
this force, we can easily compute the force that would be 
necessary to turn the rod through any other angle; for, the 
force necessary to turn it through an angle n is equal to n 
times the force necessary to turn it through the angle 1. 

When equal and opposite horizontal forces are applied 
to the two balls they both tend to turn the rod in the 
same direction, and consequently the angle through which 
the rod is turned will be the same as though a single force 
equal to the sum of the two had been applied to one of the 
balls. 



THE EARTH. 79 

Mass and Density of the Earth. 

60. Several methods have been employed to determine 
the mass of the earth, all of which depend upon find- 
ing the relation between the attraction exerted by an object 
of known mass on a given body, and the attraction exerted 
by the earth on the same body. Of these, the simplest, and 
perhaps the most reliable, is that known as the method 
of Cavendish. 

By this method the attractions exerted by two leaden 
balls is measured by means of a torsion balance, and the 
resulting acceleration is then compared with that of 
gravity. 

Explanation. A and B 
are heavy leaden balls ; CI) is 
a horizontal swinging bar; 
and EF is a vertical axis 
aronnd which the balls may be 
made to revolve by means of ^ 
the pulley G and the driving- 
belt GH. 




G 2 



I- 




F 

Fig. 31. Part of the Cavendish apparatus. 



The essential parts 
of the Cavendish ap- 
paratus are a torsion 
balance and two heavy leaden balls mounted on a horizontal 
bar so that they can be turned around an axis whose direc- 
tion coincides with the suspending wire of the balance. The 
manner in which the leaden balls are mounted and the 
method of turning them in azimuth are shown in Fig. 31. 
A horizontal plan of the apparatus is shown in Fig. 32. 

In using the apparatus the leaden balls are first brought 
to the positions P", Q", in which case they have no ten- 
dency to move the balance, and the readings of the scales K 
and L are noted. The balls are next brought into the posi- 
tions P', Q', in which case they act to turn the balance in 
the direction indicated by the arrow r heads, and when the 
instrument comes to rest, the readings of the scales are 



80 



ASTRONOMY. 



again noted. From these readings we can find the corres- 
ponding angle of torsion, that is, the angle through which 
the balance is turned by the attraction of the leaden balls. 

The swinging bar is then turned so that the heavy balls 
shall occupy the positions P, Q, symmetrical with Q', P' ; in 
this case the forces of attraction turn the balance in an 
opposite direction, and in the same manner as before the 
value of the new angle of torsion is found. 




Fig. 32. Plan of the Cavendish apparatus. 

Explanation. KL is the horizontal projection of the torsion balance, O be- 
ing the projection of the suspending wire ; at K and L are two scales of equal parts 
attached to the balls of the balance and perpendicular to KL ; T and TY are two 
fixed telescopes for reading the scales ; P and Q are the leaden balls, which can be 
so turned as to occupy either of the positions P'Q/, or P^Q". 



From these values of the angles of torsion we can, in ac- 
cordance with the principle referred to in the preceding 
article, find the force of attraction exerted by each of the 
leaden balls upon the corresponding ball of the balance. 
The distance, d, between the large and the small ball in each 
case, is known from the relation between the parts of the 
apparatus. 



THE EAKTH. 81 

If we denote the acceleration due to the attraction of a leaden ball 
at the distance d by/, the acceleration due to the earth's attraction at 
the distance R by q, the mass of the leaden ball by m, and the mass 
of the earth by M, we shall have by the Newtonian law 



m 


M 


9 & 


~d? 


' B 2 '" 


'. M=mx-x -rp 



Ail the quantities in the second member of this equation are known, 
and consequently the mass of the earth is known in terms of the mass 
of the leaden ball. 

Knowing the relative masses of the ball and the earth, and also 
their respective volumes, the average or mean density of the earth can 
be found. 

As the result of 17 experiments. Cavendish found the mean density 
of the earth to be 5.48 times that of water ; Reich of Freiburg re- 
peated Cavendish's experiments in 1836, using but one leaden ball 
instead of two, and found the mean density of the earth to be 5.438 
times that of water ; Sir Francis Baily, however, executed the most 
complete set of observations that has ever been made, in 1838-42, 
from which the mean density of the earth was found equal to 5.66 
times that of water. 

The observations made by Dr. Maskelyne, who com- 
pared the attraction of Mt. Schehallien in Scotland with 
the attraction of the earth, made the density of the earth 
equal to 4.71, and those of Prof. Airy, who compared the 
attraction of a shell of the earth with that of the entire 
earth, made the earth 's density equal to 6.56. 

From all of these results it is inferred that the mean den- 
sity of the earth is not far from 5| times that of water. 



Motions of the Earth and the Seasons. 

61. We hare already seen that the earth has two princi- 
pal motions : 1°, it rotates on an axis which maintains a 
fixed direction in space; and 2°, it revolves around the sun 
in an elliptical orbit that differs but little from a circle. 

It is in consequence of the latter motion that the sua 
appears to revolve around the earth in an elliptical orbit. 



82 



ASTRONOMY. 



The line joining the centres of the earth and sun actually revolves 
about the common centre of gravity of the earth and the sun. Now, 
whether we regard the sun's apparent motion as seen from the earth, 
or the earth's real motion as seen from the sun, the general effect is 
the same, the only difference being that the earth as seen from the sun 
is always 180° in advance of the sun as seen from the earth, both 
being referred to the stars. We may therefore speak of the sun as 
revolving around the earth, if it is understood that we only refer to 
apparent motion. 




X 




6"V 

o 




X 




Fig. 33. Parallelism of the Earth's axis. 

Explanation. M is the earth's position March 21st ; J is its position June 
21st ; S is its position September 22d ; and D is its position December 21st. In 
each case N marks the position of the north pole, and also indicates the direction 
of the earth's axis. 



Besides these motions of rotation and revolution, the 
earth is subject to certain slight motions due to the dis- 
turbing influence of the other bodies of the solar system. 
These irregular motions, which are called perturbations, 
are so small that they may be disregarded in a general view 
of the system. 

The axis of the earth is inclined to the plane of the eclip- 



THE EARTH. 83 

tic, that is, to the plane of the earth's orbit, in an angle of 
about G6° 33', and in the course of a year this axis pro- 
longed describes an oblique cylinder whose base is the 
earth's orbit and whose axis passes through the centre of 
the sun and the poles of the heavens. The plane of the 
equator being always perpendicular to the axis of this cylin- 
der, will sometimes pass through the sun, sometimes above 
the sun, and sometimes below it. 

The varying position of the equator with respect to the 
ecliptic gives rise to the changes in light and heat which 
are known as the changes of the seasons. At the 
equinoxes, that is, on the 21st of March and the 22d of Sep- 
tember, the plane of the equator passes through the sun 
and consequently the sun is on the equinoctial. From the 
21st of March to the 22d of September the plane of the 
equator passes below the sun and consequently the sun is 
north of the equinoctial, or in north declination. From 
the 22d of September to the 21st of March the plane of the 
equator passes above the sun, and consequently the sun is 
south of the equator, or in south declination. The sun is 
farthest north at the summer solstice, or on the 21st of 
June, and farthest south at the winter solstice, or on the 
21st of December. 

We have seen that the horizon of a place, not on the 
equator, divides all the diurnal circles, except the equinoc- 
tial, unequally. If the place is north of the equator, say in 
the United States, the greater part of the diurnal circle will 
be above the horizon when the circle is north of the equi- 
noctial, and below the horizon when the circle is south of 
the equinoctial. Hence, at any place in the United States 
the days and nights are equal at the equinoxes; the days 
are longer than the nights from March 21st to September 
22d ; and the nights are longer than the days from Septem- 
ber 22d to March 21st. The difference between the lengths 
of the days and nights is greatest at the solstices. 

The astronomical year is divided into four nearly equal 



84 ASTRONOMY. 

parts called seasons : the period from March 21st to June 
21st is called spring ; that from June 21st to September 
22d is called summer ; that from September 22d to De- 
cember 21st is called autumn ; and that from December 
21st to March 21st is called winter. 

It has been found by observation that the average annual tempera- 
ture of any place on the surface of the earth is nearly constant ; 
hence, we infer that all the heat which the place receives from the 
sun in the course of a year is radiated into space in the same period. 
During the day the place is both receiving and radiating heat, the 
amount received being greater than the amount radiated ; during the 
night there is no heat received, but radiation still goes on. The pro- 
cesses of receiving and radiating are so adjusted as to balance each 
other at the end of the year. 

In spring and summer the days are longer than the nights, and 
consequently more heat is received during the day than is radiated 
during the day and the night ; hence, there is a continual accumula- 
tion of heat, the accumulation being slight at the beginning of spring 
and at the end of summer. 

In autumn and winter the days are shorter than the nights and 
consequently less heat is received during the day than is radiated 
during the day and the night ; hence, there is a continual diminution 
of heat, the diminution being slight at the beginning of autumn and 
at the end of winter. 

We ought, therefore, to have our hottest weather in the latter part 
of summer, and our coldest weather in the latter part of winter. This 
would undoubtedly be the case were it not for the modifying effects 
of aerial and oceanic currents. 

In studying the subject of change of temperature, we must take 
into account the obliquity of the sun's rays : during spring and sum- 
mer the rays of the sun are, on an average, more uearly perpendicular 
to the horizon, and consequently more efficient in their heating effect, 
than they are during the autumn and winter. 

For reasons analogous to those set forth above, the hottest part of 
the day should be some time after noon and the coldest part of the 
night should be some time after midnight. 

Refraction. 

62. If a ray of light passes obliquely from one medium 
into another, it experiences a change of direction at the 



THE EAftTH. 



85 




Fig. 34. Diagram il- 
lustrating: refraction. 



common surface of the two media, and this change of direc- 
tion or bending is called refraction. 

In Fig. 34, AB represents the surface that separates the two media 
P and Q ; CD is the path of a ray in the medium P, and DE is its 
path in the medium Q, FG being normal, or perpendicular, to AB 
at D. The angle CDF is called the angle of 
incidence, EDG is the angle of refraction , and 
KDE is the refraction, or the amount of bend- 
ing. It has been shown, both by theory and 
by experiment, that under ordinary circum- 
stances the sine of the angle of incidence is 
equal to the sine of the angle of refraction 
multiplied by a constant quantity, no matter 
what may be the value of the angle of inci- 
dence. If we denote the angle of refraction 
by $' and the angle of incidence by <p, we shall have the equation 

sin <j> = m sin <j>' 

in which m is called the index of refraction. The value of m is constant 
for the same two media at the same temperature, but it is different for 
different pairs of media and also for the same two media at different 
temperatures; m is greater than 1 when light passes from a rarer to a 
denser medium, and less than 1 when it passes from a denser to a rarer 
medium, or, what is the same thing, light is bent toward the normal 
in passing from a rarer to a denser medium, and from the normal in 
passing from a denser to a rarer medium. 

The refraction, denoted by r, for the same two media increases with 
an increase of the angle of incidence, that is, the more obliquely the 
ray strikes the deviating surface the more will it be bent from its 
course. 



The Atmosphere and Atmospheric Refraction. 

63. The atmosphere is a gaseous envelope surrounding 
the earth and extending upward to a distance of 60 or 80 
miles, perhaps even to a greater height. It is a mixture 
of oxygen and nitrogen gases, together with small, but vary- 
ing, quantities of carbonic acid and watery vapor. Its den- 
sity is greatest at the surface of the earth, where it is about 
y^ as dense as water, and the density continually dimin- 



ASTROKOMY. 



ishes as we ascend. For the purpose of illustration we may 
regard it as arranged in layers concentric with the surface 
of the earth, each of which is more dense than the one next 
above it, and consequently capable of producing a greater 
amount of refraction. A ray of light falling obliquely on 
the surface of the upper stratum is bent downward, and 
this bending is continually increased as the ray passes 
from stratum to stratum till it finally 
reaches the eye of the observer ; its 
path through the atmosphere is there- 
fore a curved line, as shown in Fig. 35, 
and the apparent direction of the body 
from which the light comes is that of 
the tangent PE to the curve at the 
point where it enters the eye. Hence, 
the effect of refraction is to increase 
the apparent altitudes of the heavenly 
bodies, or, what is the same thing, to diminish their ap- 
parent zenith distances. 




Fig. 35 
refraction. 



Atmospheric 



The strata into which we have supposed the atmosphere to be di- 
vided are concentric with the surface of the earth, and because the 
height of the atmosphere is very small in comparison with the earth's 
radius, we may, without sensible error, regard the surfaces of the sev- 
eral strata as horizontal planes. 

It is to be observed that the path of a ray in passing through the 
atmosphere is usually situated in a vertical plane; hence, refraction 
produces no lateral displacement of the apparent position of a body, 
except in extraordinary cases. 



Tables of Refraction. 

64. Eefraction for a given zenith distance varies with the 
pressure, or tension, of the atmosphere, and also with its 
temperature ; it increases with an increase of pressure, and 
it decreases with an increase of temperature. Hence, in 
order to find the refraction corresponding to any observed 
zenith distance we must know the readings both of the 



THE EARTH. 87 

barometer and of the thermometer at the time of observa- 
tion. The refraction may then be found by means of tables 
called tables of refraction. 

Several different formulas have been deduced for determining the 
amount of refraction corresponding to any observed zenith distance, 
or altitude, but they are all somewhat complex. 

A complete set of Bessel's tables, with full directions for using, is 
to be found in Loomis' Practical Astronomy, to which work the stu- 
dent is referred for further information. 

It is to be observed that the tables are not very reliable when the 
apparent zenith distance exceeds 80° ; beyond this limit the irregular- 
ities of refraction are too great to be brought within the scope of any 
formula. These irregularities increase as we approach the horizon, 
and it is within the narrow zone near the horizon that we are to look 
for lateral refraction and other disturbances which sometimes result 
in peculiar distortions of the disks of the sun and moon. 

Some Effects of Refraction. 

65. The general effect of refraction is to throw all the 
heavenly bodies toward the zenith, and this effect is in- 
creased as we approach the horizon. 

One of the most notable consequences of refraction is a 
lengthening of the amount of sunlight at any place. Re- 
fraction at the horizon is nearly 35'; hence, the sun 
appears to rise earlier and to set later than it would were 
it not for the atmosphere. This increase, at the equator, 
amounts, to more than 4 minutes per day. On an average 
over the entire globe the increase amounts to about T ^-g- 
part of the whole period of sunlight. 

Another effect is to distort the forms of the disks of the 
sun and the full moon when near the horizon. The refrac- 
tion being greater at the lower than at the upper limbs of 
these bodies, the lower limbs are thrown up more than the 
upper ones, and thus gives the bodies an oval shape, which 
is very obvious at all times, but occasionally, in conse- 
quence of extraordinary refraction, the flattening is pecu- 
liarly striking. 



88 ASTRONOMY. 

Twilight. 

66. After sunset and before sunrise the solar rays illumi- 
nate a part of the earth's atmosphere, giving rise to a dif- 
fused light that we call twilight. Evening twilight begins 
at sunset and gradually grows fainter till it finally becomes 
extinct when the sun has descended to about 18° be]ow the 
horizon ; morning twilight begins when the sun has risen 
to within 18° of the horizon and gradually grows brighter 
till sunrise. 

The length of twilight varies in different latitudes, and 
also in the same latitude at different seasons of the year, 
but the length of the evening twilight is always equal to 
that of the succeeding morning twilight. 

The length of evening twilight at the equator does not 
differ much from 1J- hours, and is nearly constant through 
the year; in the latitude of New York it varies from 1J to 
2 hours, the shortest twilight being in winter and the long- 
est in summer ; at all places north of latitude 49°, as, for 
example, in all parts of Great Britain, the sun does not 
descend as much as 18° below the horizon at the time of the 
summer solstice, so that morning twilight begins before 
evening twilight ends, and consequently twilight lasts all 
night ; at the north pole evening twilight begins about the 
22d of September, when the sun passes below the horizon, 
and lasts till about the 12th of November, at which time 
the sun is 18° south of the equinoctial, that is, it lasts for 
more than 50 days, and the morning twilight has a corre- 
sponding duration. 

The cause of the variation in the' length of twilight is 
found in the different degrees of obliquity of the sun's 
diurnal path to the horizon. When the sun sets, or rises, 
obliquely to the horizon, a longer time is occupied in de- 
scending or ascending through a vertical distance of 18° 
than when it sets perpendicularly to the horizon. 



THE EAKTH. 



Parallax. 



67. Parallax is a change in the apparent direction of a 
body due to an actual change in the position of the point 
from which the body is observed. 

An idea of what is meant by parallactic displacement may be ob- 
tained as follows: let the student hold a pencil vertically between 
his face and a vertical wall which is ten or twelve feet distant ; then, 
without changing the position either of his head or of the pencil, let 
him first close the right eye and note the apparent place of the pencil on 
the wall as seen by the left eye ; again, closing the left eye and 
opening the right one, let him note the apparent place of the pencil 
on the wall ; the pencil will appear to have moved from right to left 
along the wall. This apparent change of place is the parallactic dis- 
placement of the pencil, due to a change in the position of the point 
of observation from one eye to the other. 

68. Geocentric parallax is the change that the ap- 
parent direction of a body would experience if the point of 
observation were changed from the surface of the earth to 
its centre. 



Explanation. O is the point from 
which the hody M is observed ; C is the 
centre of the earth ; Z is the zenith of O, 
and ZOM, equal to z', is the observed 
zenith distance of M ; and OMC, equal to 
p, is the geocentric parallax of M. 

In Fig. 36 the body M as 
seen from appears to lie in 
the direction OM, but if seen 
from C it would appear to be 
in the direction CM. The 
angle OMC is therefore the 
geocentric parallax of M, and 

it is obviously equal to the angle subtended by the radius 

OC, at the body M. 
It is plain, from the figure, that the zenith distance of a 




Fig. 36. Geocentric Parallax. 



90 ASTRONOMY. 

body seen from the surface of the earth is greater than it 
would be if seen from the centre, the difference being equal 
to its geocentric parallax. 

The geocentric parallax of a body depends upon its apparent zenith 
distance, and also upon its actual distance from the centre of the earth. 
To deduce the law of variation, let us denote ZOM by z' , OMC by p, 
or CM by D and OC by R ; then, because the sides of a triangle are 
proportional to the sines of their opposite angles, and because the sine 
of the angle COM is equal to the sine of z', we have 

■p 

D : R : : sin z' : sin p ; whence, sin^=- sin z / (1). 

Hence, we see that the sine of the parallax varies directly as the sine 
of the apparent zenith distance of the body, and inversely as its actual 
distance from the centre of the earth. 

The parallax of a body is zero at the zenith and it is greatest at the 
horizon ; in the latter case it is called the horizontal parallax; in all 
other cases it is called parallax in altitude. 

If we make z' =90° in equation (1) and denote the corresponding 
value of p by P, we have 

sin P= R . (2) ; whence D=:-JL (3). 

D sin P 

From equation (2) we see that P depends on both R and D ; if R is 
the equatorial radius of the earth, and if D is the mean distance of the 
body from the earth, the corresponding value of P is called the mean 
equatorial parallax. In speaking of the sun, this angle is usually 
designated by the simpler term solar parallax. 

Equation (3) enables us to find the mean distance of a body from 
the earth when we know its mean equatorial parallax and the radius 
of the earth. 



69. Heliocentric parallax is the change that the ap- 
parent direction of a body would experience, if the point of 
observation were transferred from the centre of the earth to 
the centre of the sun. 

In Fig. 37, EM is the direction of the body M as seen 
from E, and SM is its direction. as seen from S; hence, 
EMS, which is equal to KEM minus KSM, is the heliocen- 




THE EARTH. 91 

trie parallax of M, and it is obviously equal to the angle 
subtended by the earth's radius-vector SE as seen from M. 



Explanation. E represents the centre of the 
earth. S that of the suu, and M that of a heavenly 
hocly, say Mars. The directions in which the earth 
and Mars are moving are represented by the arrow 
heads. 

The use of the heliocentric parallax of a 
body is to determine the motion of a body 
as it would appear from the sun. 

The angle KEM, which is the supplement 
of SEM, is found by observation. The an- 
gle EMS, or the heliocentric parallax, is 
found from the formula 

QTTi Fig. 37. Heliocentric Parallax. 

sin EMS =— sin KEM.... (4), 
SM V 

which is deduced in the same manner as formula (1) in the preceding 
article. The angle KSM is then found by subtracting the angle EMS 
from the angle KEM. 



70. The animal parallax of a star is the apparent 
displacement of the star due to the earth's annual revolution 
around the sun. 

If we conceive a straight line to be drawn from the earth 
passing through a star, this line will in the course of a year 
generate the surface of a cone whose vertex is the star and 
whose base is the earth's orbit ; the axis of this cone will 
in general be oblique to plane of the earth's orbit. If we 
suppose all the elements of the cone to be prolonged to the 
celestial sphere they will meet it in an ellipse which will be 
the apparent path of the star due to parallax; the centre 
of the ellipse will be the position of the star as seen from 
the sun. If the' axis of the cone is perpendicular to the 
plane of the ecliptic, the ellipse becomes a circle ; if the 
axis lies in the plane of the ecliptic, the ellipse becomes a 
straight line. 

The angle at the earth subtended by the semi-transverse 



92 



XSTROtfOMy. 



axis of the ellipse, which is equal to the angle at the star 
subtended by that semi-diameter of the earth's orbit 
which is perpendicular to the axis of the parallactic cone, is 
called the stellar parallax. When this angle can be 
found, we can immediately compute the distance of the star 
from the sun or from the earth. 




Explanation. S represents the sun ; E the earth in its or- 
S' bit ; and S' the star. SS' is the axis of the parallactic cone ; SE 
is the radius-vector of the earth's orbit which is perpendicular 
to SS' : and ES'S is the stellar parallax, denoted by p. 

In the right-angled triangle SS'E we have, since 
ES'S is a very minute angle, 
.SE 
~P 



SS' 



.(5). 



Fig. 38. Annual or 
Stellar Parallax. 



Mauy attempts have been made to find the 
stellar parallax, but, except in the case of a 
few stars, they have been unsatisfactory. The 
largest stellar parallax that has been found is 
that of a Centauri, a southern star. Its par- 
allax is a little less than 1" of arc, which cor- 
responds to a distance of about 20 millions of millions of 
miles. This almost inconceivable distance is so great that 
light traveling at the rate of 186,360 miles a second would 
require more than 3 years to traverse the space that sep- 
arates the star from the earth. The distance of a Centauri 
from the sun is, according to Newcomb, about 221,000 
times as great as that of the earth from the sun. 

Newcomb says, "the recent researches of various ob- 
servers have resulted in showing that there are about a 
dozen stars visible in our latitudes of which the parallax 
ranges from a tenth to a half second." The corresponding 
times required for light to come from these stars to the earth 
would therefore range from 30 down to 6 years. The bright 
star a Lyras has, according to Dr. Biunnow, a parallax of 
about one-fifth of a second, which corresponds to a distance 



THE EARTH. 93 

which is more than a million of times as great as that of 
the earth from the sun. 

All attempts to find any appreciable parallax for the stars which 
are visible to the naked eye, except in a few instances, have totally 
failed, and we are permitted to assert that their distances from us are 
not measurable. What then shall be said of the countless millions of 
stars that are revealed to us by our powerful telescopes ? It has been 
conjectured that some of these bodies are so far distant that their light 
can only reach us after a flight of hundreds, perhaps thousands, of 
years. 

Aberration. 

71. Aberration is a displacement in the apparent place 
of a body due to the combined motion of the observer and 
of light. 

It is analogous in effect to the combined motion of an 
observer in a railway car and that of a falling drop of rain. 
If a shower of rain is falling on a still day, and if the ob- 
server is at rest, he will see the drops descend in vertical 
lines ; but if he is moving in a rapidly advancing car, he 
will see the drops descend obliquely, and as though they 
had come from a point in advance of his position. 

Explanation. DA represents the velocity of a ray of light and r» 
the direction of its motion ; OA represents the velocity of the ob 
server and the direction of his motion ; and DC is equal and par- 
allel to AO. 

In accordance with the law of relative motion, 
the apparent path of the rain-drop is the same 
that it would be if the observer were at rest and 
the drop were, in addition to its actual motion, 
endowed with a motion equal and directly oppo- 
site to that of the observer. 

In like manner the combined motion of the observer and 
of a ray of light causes a body to appear as if thrown slightly 
forward in the direction of the observer's motion. If in 




94 ASTRONOMY. 

Fig. 39 we suppose the observer to be at rest and the 
light to move with the combined velocities DA and DC, it 
will reach in the direction of the diagonal of the parallel- 
ogram described on DA and DC. The body from which 
the light comes will appear to be thrown forward, the dis- 
placement being equal to the angle COD. The angle COD 
is called the aberration, and its value will be the greatest 
possible when DA is perpendicular to OA. 

If we denote the aberration in this case by a, we have from the 
right-angled triangle OCD 

DC 

tana=-, 

or because the angle a is very small, we have the formula 

«=7 CO 

In which v is the velocity of the observer and V the velocity of light. 
Hence, the maximum value of aberration is equal to the velocity of the 
earth in its orbit divided by the velocity of light. This value, which has 
recently been found to be equal to 20". 49, is sometimes called the 
constant of aberration. 

Explanation. Same as before, except that the direc- 
tion of light is inclined to that of the observer's motion 
in an angle EAD denoted by I', equal to I. 

In Fig. 40, the angle CDO is equal FCO - a' ; 
but a' is so small that we may regard CDO equal 
to FCO or to I. We then have from the trian- 
gle OCD the proportion 

v : V : : sin a' : sin I . . (2) 

v 
If we replace sin a' by a' and — by 20". 49, 




we have, from (2) 



a' = 20". 49 sin I (3) 



Hence, the general value of aberration varies as the sine of the incli- 
nation of the direction of light to the direction of the observer's motion. 

When the observer is moving directly toward or directly from a 
body the aberration is zero ; when he is moving at right angles to the 



THE EARTH. 



95 




motion of light the aberration is 20". 49 ; in all other cases the aberra- 
tion lies between these limits. 

Explanation. S is the sun ; ACDF is the 
orhit of the earth ; s is a star at the pole of the 
ecliptic ; and acdf is the annual curve of aber- 
ration. 

In Fig. 41, let s be the true place of 
a star, at the pole of the ecliptic. When 
the earth is at A the star is thrown 
forward in the direction sa, parallel to 
the earth's motion, and to a distance 
equal to 20' '.49 ; when the earth is 
at C the star is apparently at c, sc 
being equal to 20". 49 ; when the earth 
is at D the apparent place of the star is 
d ; and when the earth is at F the ap- 
parent place of the star is at/. Hence, 
we see that the star appears, in conse- 
quence of aberratiou, to describe a circle 

around its true place ; the time of description being a year, and the 
spherical radius of the circle being equal to 20". 49. 

If the star is obliquely situated with respect to the ecliptic it will 
appear to describe an ellipse whose semi-transverse axis is 20". 49 and 
whose semi-conjugate axis is 20".49 multiplied by the sine of its celes- 
tial latitude. 

If the star is in the plane of the ecliptic it will oscillate back and 
forth along a line in the ecliptic whose middle point is the true posi- 
tion of the star, and whose length is 40". 98. 

In all cases the true position of the star is at the centre of its appar- 
ent annual path. 

The sun at every instant appears to be moving in space in exactly 
the opposite direction to that of the earth's actual motion ; hence, the 
effect of aberration is to cause the sun to appear 20". 49 behind its true 
place. 



Fig. 41. Aberration at the 
pole of the Ecliptic. 



Precession and Nutation. 

72. It has been stated (Art. 12) that the equinoxes have 
a slow motion from east to west along the ecliptic, which 
is called the precession of the equinoxes. This motion, 
averaging 50". 2 a year, is produced by the unequal attrac- 



96 ASTRONOMY. 

tions of the sun and of the moon on the different parts of 
the equatorial protuberance (Art. 57). Most of the matter 
of this protuberance lies in the equatorial regions, and for 
the purposes of explanation we may regard it as a ring 
whose central plane coincides with the plane of the equator. 



Fig. 42. Precession of the Equinoxes. 



Explanation. In this figure the plane of the paper passes through the centres 
of the sun and earth, and is perpendicular to the plane of the ring. CS is in the 
projection of the ecliptic, S heing the centre of the sun; EQ is the projection of the 
ring, C being the centre of the earth ; CP is the acceleration due to the sun's attrac- 
tion at C ; EP' is that due to the sun s attraction at E ; and QP" is that due to the 
sun's attraction at Q. 

Because E is nearer to the sun than C is, EP' is greater than CP ; 
for a like reason CP is greater than QP". If we resolve EP' into two 
components, one of which, EA, is equal and parallel to CP, the other 
one will have the direction EF parallel to the line joining A andP' 
(Peck' s Mechanics, Art. 26) ; in like manner if we resolve QP" into 
two components, one of which, QB, is equal and parallel to CP, the 
other will have a direction, QD, parallel to the line joining B and P". 
Now, the forces CP, EA, and QB, being parallel and equal, it is obvi- 
ous that their effect is simply to draw the masses C, E, and Q in paral- 
lel lines toward S. The remaining forces EF and QD, which are small 
in comparison with CP, will act to produce rotation of the ring, and 
consequently of the whole earth, around an axis perpendicular to the 
plane ECS at C. This rotation, combined with the earth's rotation on 
its axis, produces a retrograde motion of the line of equinoxes, in ac- 
cordance with the law of composition of rotations (Mech., Arts. 142-3). 
The attraction of the moon on the ring acts in like manner, bat with 
greater effect, to produce a retrogradation of the equinoxes, and a very 
slight effect of the same kind is also produced by. the action of the 
planets The action of the sun in producing precession is variable, 
in consequence of the different aspects of the ring as seen from the 
sun : it is greatest about the times of the solstices, and least about the 
times of the equinoxes, going through all its changes in a year. The 



THE EARTH. 97 

action of the moon is still more variable. It goes through its principal 
changes in a nodical period, but, as we shall see hereafter, the plane 
of the moon's orbit is continually changing its position with reference 
to that of the equinoctial, completing its cycle of change in about 18.6 
years. There is therefore an inequality in the precession extending 
over this cycle, during which the pole of the heavens recedes from 
and approaches the pole of the ecliptic, the entire arc of oscillation 
amounting to about 19". This inequality is known as the nutation of 
the earth's axis. 

In consequence of the combined effects of precession and nutation, 
for they are always considered together, the pole of the heavens retro- 
grades around the fixed pole of the ecliptic in a slightly waving line, 
that may for our purposes be regarded as a circle, whose spherical 
radius is about 23° 27 r . The cycle of a complete revolution of the 
axis of the earth about that of the ecliptic is 25,800 years. 

Effects of Precession and Nutation. 

73. The effect of precession and nutation is to produce a 
continual change in the right ascensions and declinations of 
the stars. This change is caused by the displacement of the 
equinoctial and of the vernal equinox, to which the positions 
of the stars are referred. When we know the right ascen- 
sion and declination of a star at a given epoch, we can find 
these elements at any other time by means of formulae and 
tables constructed for the purpose. 

The continued change in the right ascensions and declina- 
tions of the stars produces a slow but progressive change in 
the aspect of the heavens ; the north pole of the heavens, 
continually changing place, comes successively into the 
neighborhood of new stars, which in turn become pole-stars. 
The diurnal circles of all the stars gradually change to con- 
form to the new position of the pole, and the positions of 
the constellations with respect to the poles of the heavens 
experience a corresponding change. 

After the lapse of about 12,000 years, according to Her- 
schel, the bright star a Lyras will be within 5° of the pole, 
and will therefore be the pole-star, and at that time the 
present north-star w 7 ill be more than 40° from the new pole. 



98 ASTEOKOMY. 

About 4000 years ago, that is, about the time of the build- 
ing of the pyramids of Egypt, the north pole of the heavens 
was about 3j° from the bright star a Draconis, which was 
at that time the pole-star. In this connection we condense 
from ISir John Herschel the following curious facts relat- 
ing to the pyramids of Gizeh. The latitude of Gizeh being 
30° N., the star in question must have had its lower culmi- 
nation at an altitude of about 26|°. The explorations of 
Col. Vyse show that of the nine pyramids still existing at 
Gizeh, six (including the largest) have the narrow passages 
by which alone they can be entered (opening on the north- 
ern faces) inclined downward at angles varying from 26° 2' 
to 28°, the average inclination being about 26° 47'. " At 
the bottom of every one of these passages, therefore, the 
then pole-star must have have been visible at its lower cul- 
mination, a circumstance which can hardly be supposed to 
have been unintentional, and was doubtless connected (per- 
haps superstitiously) with the astronomical observation of 
that star, of whose proximity to the pole at the epoch of 
the erection of these wonderful structures, we are thus 
furnished with a monumental record of the most imperish- 
able nature." 

Micrometers. 

74. The filar micrometer is a contrivance for measur- 
ing the angular distance between two objects, both of which 
are in the field of view of the telescope. When an addi- 
tional arrangement is made for measuring the angle in- 
cluded between the line that joins the two objects and the 
hour circle passing through one of them, the instrument is 
called a position micrometer. 

The simple filar micrometer consists essentially of two 
parallel wires, or spider lines, placed at the common focus 
of the objective and the eye piece, and so mounted that 
they can be moved at right angles to their lengths by means 



THE EARTH. 



99 



of two. delicate screws of uniform pitch, called micro- 
meter screws. The interval between the wires, in terms 
of the distance between two consecutive threads of the 
screw can be read oh* by means of a suitable scale, and from 
this the angular distance between them can be found by 
a simple computation. 

In the position micrometer the part just described is 
mounted so that it can be revolved around the line of col- 
limation as an axis, and a graduated circle with an index 
is introduced for measuring the angle through which it is 
turned. 



M 




Fig. 43. The Position Micrometer. 



Description. In Fig. 43, aa is a longitudinal wire attached to the 
perforated diaphragm of the instrument in such manner that it always 
intersects the line of collimation at right angles. The parallel wires 
c and d are perpendicular to aa, the former being attached to the slid- 
ing fork F, and the latter to the sliding fork H. These forks termi- 
nate in screws, and may be moved to and fro by the nuts, or screw 
heads, M and N, which are so arranged as to admit of rotary motion 
only ; the number of entire turns of either screw head is shown by a 
serrated scale, bb, at the bottom of the opening of the diaphragm, 
each notch of which corresponds to one turn. The circular, or flange- 
like, projections Gr and K, are each divided on their circumferences 
into 100 equal parts, and by means of suitable indices they indicate 
the number of hundredths of a turn. The middle of the serrated scale 
is indicated by a small hole, and when either of the parallel wires 



100 ASTRONOMY. 

bisects it, that wire intersects aa in the line of collimation ; thus, in 
the figure the point s is in the line of collimation. 

The circle CC, whose graduation is not shown, is called the position 
circle ; when the instrument is revolved about the line of collimation 
the point .<? remains fixed, and the arc of the position circle which 
passes by the index determines the angle through which the line aa 
is revolved. 

Before using the position micrometer we must know the polar read- 
ing of the position circle and the angular value of one turn of the 
screw head. 

To find the polar reading, the telescope is directed to an equatorial 
star and the micrometer is revolved in the direction of the graduation 
till the star appears to move along the longitudinal wire aa ; the 
corresponding reading diminished by 90° is the polar reading, that is, 
it is the reading of the position circle when aa coincides with an hour 
circle. To find the angular value of one turn, set the wires c and d 
so that they shall be at a distance apart equal to say 20 notches ; 
then turn the telescope to an equatorial star and note the sidereal 
time required for it to pass from one wire to the other ; convert this 
time into angular measure and divide by 20 ; the quotient will be the 
angular value of one turn. 

As an example of the use of the instrument, let it be required to 
measure the distance from the star s to the star s f , and the inclination 
of ss' to the hour circle through s. Having brought the wire c to the 
zero of the scale bb, direct the telescope so the star 6- shall be at the 
intersection of c and aa ; turn the micrometer on its axis till aa passes 
through s' ; then move the wire d till it coincides with s'. To the 
number of entire turns indicated on the scale bb, add the hundredths 
of a turn as shown by the graduation on the screw head, and multiply 
the result by the angular value of one turn ; the result will be the 
angular distance ss'. 

From the reading of the position circle (increased by 360° if neces- 
sary) subtract the polar reading of the instrument; the remainder 
will be the angle between the hour circle and the line ss'. 



The Zenith Telescope. 

75. A zenith telescope is a telescope arranged for 
measuring small differences between the meridian zenith 



THE EAKTH. 



101 



distances of two stars. It consists of a telescope, having a 
filar micrometer at the common focus of its objective and eye 
piece, and so mounted that it can be turned around either 
a vertical or a horizontal axis. In the form now used on 
the IT. S. Coast Survey, the mounting is similar to that-of 
the portable transit, which permits the instrument to be 
used in place of a transit. The mounting differs however 
from that of a simple transit in the fact that the piers 
which carry the horizontal axis, instead of resting on a solid 
support, are attached to a horizontal plate which can be 
turned in azimuth upon a second horizontal plate, much as 
the vernier plate of a theodolite is turned on the horizontal 
limb. The telescope is provided with a circle and level by 
means of which its line of collimation may be set so as to 
make any angle with the vertical, and the revolving hori- 
zontal plate has a clamp and tangent screw by means of 
which the instrument can be brought into the plane of the 
meridian. This* plate has also two movable stops which 
can be set at the opposite ends of a diameter. When the 
stops are set, the instrument can be reversed, that is, it can 
be turned 180° in azimuth, without the trouble of reading 
the circle at each reversal. 




To explain the use of this in- 
strument, let E be the place of the 
observer ; Z bis zenith ; HZH' the 
meridian of E ; s and s' the points of 
culmination of two stars, whose right 
ascensions differ by only a few min- 
utes of time. We also suppose that 
the distances Zs and Zs" to be approx- 
imately known, and that they differ 
but little from each other. 

The instrument having been placed in the meridian and the stops 
set, the telescope is directed so that its line of collimation shall incline 
towards the south and make an angle with the vertical equal to the 
mean of the assumed zenith distances of s and s'. Suppose EA to be 
the position of the line of collimation when the instrument is turned 



Fig. 44. Method of using the 
Zenith Telescope. 



102 ASTRONOMY. 

towards the south, and EC to be its position when turned towards the 
north ; also supposs that s culminates a few minutes before s'. The 
micrometer having been placed so that its longitudinal wire shall be 
in the plane of the meridian, the angle As is measured at the instant 
s crosses the meridian ; the instrument is then reversed and when s' 
crosses the meridian the angle CV is measured, both measurements 
being made as explained in Art. 74. 

Denoting the angle ZEA or its equal ZEC by <j>, the meridian zenith 
distance of s by z, and that of s' by z', we have from the figure, 

z = <p — As, and z' — <j> + (Y . . . . (1) 

whence, by subtraction, 

z' -z = Cs' + As (2) 

but in practice it is customary to call distances estimated from a star 
toward the zenith positive, in which case those estimated in a contrary 
direciiotfare negative. Adopting this notation the arc Cs' is essentially 
negative, and equation (2) takes the form 

z'-z = As-Cs' (3) 

If one of the parallel wires is set to mark the point of culmination of s 
and the other to mark the point of culmination of V the angular dis- 
tance between them will be the value of z' — z. 

Different Methods of Finding Latitude. 

76. In Art. 10 the latitude of a place is defined to be its 
angular distance from the equator. Referring to the figure 
and accompanying explanation in that article, we see that 
the latitude of the place a is equal to QEZ, which is the 
complement of PEZ ; hut HEZ being a right angle, HEP 
is also the complement of PEZ ; and consequently HEP is 
equal to QEZ. Hence, the latitude of a place is equal either 
to the declination of its zenith, or to the altitude of the ele- 
vated pole, that is, of the pole which is above the horizon. 
The methods of finding the latitude of a place are simply 
methods of finding one or the other of these two angles. 
Some of these methods are given below. 

First method. Let E be the place of the observer; 
HZH' the upper branch of his meridian ; P the elevated 



THE EARTH. 



103 




Fig. 45. 
Latitude. 



Method of finding 



pole ; EQ the projection of the equinoctial on the meridian ; 
and let s" and s'" be the points of upper and lower culmination 
of a star which is near the pole. 

The altitudes B.s" and HV" are 
measured with some suitable in- 
strument, and both are corrected 
for refraction. Then, because the 
distance of the star from the pole 
is the same for each observation, 
HP, or the latitude, is equal to 
the half sum of the corrected altitudes. 

If the polar distance of the star, Ps" or Ps'", is known, 
the latitude may be found by a single observation. 

Second method. Let E be the place of the observer ; 
Z his zenith ; HZH his meridian ; S the place of a star 
whose declination is known ; 
ZSB a vertical circle through S ; 
and PS an hour circle. Also, 
let HBH be the celestial hori- 
zon of the observer at E. The 
altitude BS is measured and the 
sidereal time of observation is 
noted. The measured altitude 
is first corrected for refraction, 
and the result taken from 90° ; 

this gives the arc ZS ; the difference between the sidereal 
time of observation and the right ascension of S gives the 
hour angle ZPS ; the declination of S being subtracted 
from 90°, gives the value of PS. In the spherical triangle 
ZPS we therefore know the sides ZS, PS, and the angle 
ZPS ; hence the side PZ may be computed. But, PZ is 
the complement of the latitude; the latitude may there- 
fore be f ouud by subtracting PZ from 90°. 




Determination of Lati- 



The spherical triangle ZPS, in which S is any star, is often called 
the astronomical triangle, on account of its importance in astronomi- 



104 ASTBOHOMY. 

1 

cal computations. In it, PZ is the co-latitude of the place of observa 
tion ; ZS is the zenith distance of the star ; PS is the star's polar dis- 
tance ; ZPS is the hour angle of the star; PZS is the azimuth of the 
star counted from the direction of the elevated pole ; and PSZ is called 
the position angle of the zenith. When any three of these elements of 
the triangle are known, all the others may be found by computation. 

Third method. This method was first employed by 
Capt. Talcott, of the U. S. Army, and is generally known 
as Talcott' s method. It is the simplest and the most 
accurate of all the methods, but it is only applicable when 
an approximate value of the latitude is already known. 

Explanation. An approximate value of the latitude being known, 
we select from a catalogue two stars which culminate within a few min- 
utes of each other and whose meridian zenith distances are nearly 
equal. Let s and s' , Fig. 44, be the points at which these stars cul- 
minate, EQ being the projection of the equinoctial and Z being the 
zenith of the place whose latitude is to be determined. 

Denote QZ, which is equal to the latitude, by I ; Qs, Qs', which are 
the declinations of the stars, by d and d' ; and Zs, Zs', which are the 
meridian zenith distances of s and s' , by z and z' . We then have, 
from the figure, 

I = d + z ; and I = d' - z> (1) 

Adding equations (1), member to member, and dividing by 2, we have 

l = i(d+ d') - \{z> -z) (2) 

The value of d + d' is found from the star catalogue, the value of 
z' — z is found by the method explained in Art. 75, and these values 
substituted in equation (2) give the latitude required. 

Geocentric Latitude. 

77. The latitude determined by any of the preceding 
methods is called the geographic latitude, and is equal 
to the angle between the normal at the place and the plane 
of the equator. The geocentric latitude is the angle 
between the radius of the earth at the place and the 
plane of the equator. The angle between the normal and 



THE EARTH. 



105 



the radius is called the reduc- 
tion ; this is zero. at the equa- 
tor and at the poles, and is a 
maximum when the latitude is 
45°, where it is about 11' 30". 



Explanation. The ellipse PMQE is the 
meridian of the place M ; EQ, the equator ; 
MA, the normal at M ; MC, the radius at M ; 
QAM, the geographic latitude of M ; QCM, 
its geocentric latitude ; and AMO, the re- 
duction. 




Fig. 47. Geocentric Latitude. 



Apparent and Mean Solar Time. 

78. An apparent solar day is the interval between two 
successive transits of the sun over the upper branch of the 
same meridian ; time reckoned in terms of this unit is called 
apparent solar time. 

This species of time is not adapted to the wants of astron- 
omy because it is not uniform. The sun's motion along the 
ecliptic is variable, and furthermore, the direction of its 
motion w T ith respect to the equinoctial is continually chang- 
ing ; for these reasons the sun's advance in right ascension 
is not uniform, and consequently the lengths of apparent 
solar days are not equal to each other. 

To secure the desired uniformity, astronomers have 
adopted the device of an imaginary sun, moving uniformly 
along the equinoctial and making the circuit of the heavens 
in the same time as the real sun ; this imaginary body is 
called the mean sun. The interval between two consecu- 
tive transits of the mean sun over the upper branch of the 
same meridian is called a mean solar day, and time reck- 
oned in terms of this unit is called mean solar time. 

The manner in which the motion of the mean sun is con- 
nected with that of the true sun may be explained as fol- 
lows. We first suppose a fictitious sun to move uniformly 
along the ecliptic, its rate of motion being equal to the 



106 ASTRONOMY. 

real sun's average motion m longitude. This fictitious sun 
coincides with the real sun when the earth is in perihelion 
and when it is in aphelion, but at no other time. The 
longitude of this imaginary body is called the sun's mean 
longitude, and its angular motion with respect to the 
earth is called the sun's mean motion in longitude. 
When this fictitious sun reaches the vernal equinox, a 
second fictitious sun is supposed to start from that point 
and to move uniformly along the equinoctial with the same 
angular velocity as the first ; the two fictitious suns are to- 
gether at the equinoxes, but at no other times. This second 
fictitious sun is the mean sun of astronomy. 

Because the longitude of the first fictitious sun is zero when it is at 
the vernal equinox, and because the two imaginary suns have the same 
angular velocity, it is obvious that the right ascension of the mean sun 
is always equal to the sun's mean longitude. 

The Equation of Time. 

79. The equation of time is the difference between ap- 
parent and mean solar time at any instant. 

The equation of time is used to convert apparent into 
mean solar time; it is also used to convert mean into appar- 
ent solar time. When the mean sun is west of the true sun 
it comes to the meridian before the true sun and the equa- 
tion of time is positive, that is, it must be added to appar- 
ent time to get mean time ; when the mean sun is east of 
the true sun it comes to the meridian after the true sun 
and the equation of time is negative, that is, it must be sub- 
tracted from apparent time to get mean time. 

The value of the equation of time for every day in the 
year, with the rule for using it, is given in the Nautical 
Almanac. It is equal to zero four times a year ; viz. : on 
the 15th of April, on the 14th of June, on the 1st of Sep- 
tember, and on the 24th of December. It has its greatest 
itive value on the 11th of February, at which time it 




THE EARTH. 107 

amounts to more than 14 minutes, and its greatest negative 
value on the 2d of November, when it amounts to more than 
1G minutes. At the former time the forenoons are nearly 
half an hour shorter than the afteruoous, and at the latter 
time the afternoons are more than half an hour shorter than 
the forenoons. These irregularities take place when the 
days, in the northern hemisphere, are very short, and for 
this reason they are particularly noticeable. 

Explanation. The figure repre- 
sents the projection of a part of the 
celestial sphere on the plane of the 
meridian HZH ; P is the elevated pole ; 
EQ, is the projection of the equinoctial ; 
VS is the projection of the ecliptic ; PS' 
and PM are projections of hour circles, 
the former passing through the true 

sun S, and the latter through the mean n ' r" 

sun M, hoth being west of the me- 
ridian. Fig. 48. Apparent and Mean Time. 

The nature of the equation of time and the method of 
applying it will be understood after a careful study of Fig. 48. 
The hour angle QPS, measured by the arc QS', is the angle 
between the meridian and the hour circle through the true 
sun ; hence, QS' divided by 15° is the apparent time at 
the instant in question. The hour angle QPM, measured 
by the arc QM, is the angle between the meridian and the 
hour circle through the mean sun ; hence, QM divided by 
15° is the mean time at the instant in question. The dif- 
ference between QS' and QM, that is, the arc S'M divided 
by 15° is the equation of time. In the case considered the 
equation of time is positive, and it is obvious from the 
figure that the mean time is equal to the apparent time 
plus the equation of time. 

The arc VS' is the right ascension of the true sun, and the arc VM 
which is the right ascension of the mean sun is, from Art. 78, the 
sun's mean longitude. Hence, the equation of time is the difference 
between the sun's true right ascension and his mean longitude. 



108 ASTKONOMY. 



Comparison of Sidereal and Mean Solar Time. 

80. The meridian plane of any place is carried eastward 
by the earth's rotation, sweeping uniformly over the 
heavens, and indicating the lapse of time by its progress 
amongst the stars. In a sidereal day it turns through an 
angle of 360°, but in a mean solar day it turns through an 
angle which is greater than 360° by an amount which is 
equal to the angular motion of the mean sun in that time. 

From what has preceded it is plain that the number of 
sidereal days in the interval between two successive returns 
of the sun to the vernal equinox is greater by 1 than the 
number of solar days in the same period. This interval is 
called a tropical year, and as we shall see hereafter it con- 
tains 365.2422 mean solar days; hence, it must contain 
366.2422 sidereal days. 

The quotient of 366.2422 by 365.2422 is 1.002738 nearly, and the 
quotient of 365.2422 by 366.2422 is .99727 nearly. Hence, a mean 
solar day is equal to 24 hoars, 3 minutes. 56.56 seconds of sidereal 
time, and a sidereal day is equal to 23 hours, 56 minutes, 4.13 seconds 
of solar time. 

The solar day exceeds the sidereal day by 3 minutes, 56.56 seconds 
of sidereal time, or by 3 minutes, 55.9 seconds of solar time. 

In practice intervals of solar time are converted into corresponding 
intervals of sidereal time, and the reverse, by means of tables con- 
structed in accordance with the preceding principles. 

Astronomical Dates. 

81. The time at which the apparent sun crosses the 
upper branch of the meridian of any place is called ap- 
parent noon, and the time at which the mean sun crosses 
the meridian is called mean noon. The astronomical 
day begins at one mean noon and ends at the next mean 
noon, the interval being divided into hours, minutes, and 
seconds as already explained (Art. 17). The date of any 



THE EARTH. 109 

astronomical day is the same as that of the civil day on 
which it begins ; its hours are numbered contiuuously up to 
24. Thus, the day that begins at noon on the 22d of 
December ends at noou on the 23d of December, and, in 
astronomical language, this interval is styled the 22d of 
December. The astronomical date December 22d, 6 hours 
15 minutes, corresponds to the civil date December 22d, 
6 hours 13 minutes, p. m.; the astronomical date December 
22d, 18 hours 13 minutes, corresponds to the civil date 
December 23d, 6 hours 13 minutes, a. m. 

It is the custom for each astronomer to reckon time from the instant 
when the mean sun crosses his own meridian ; time thus reckoned is 
said to be local time. It is obvious that the absolute instant of time 
at which a phenomenon is observed may bear different dates at dif- 
ferent places. In order, therefore, that we may compare the observa- 
tions of different astronomers, we must not only know the local dates, 
but also the relative positions of the places of observation. 

The Chronometer. 

82. In many cases it Avould be inconvenient to use an 
astronomical clock (Art. 18), and in some cases, especially 
at sea, its use would be impossible. In these cases a chro- 
nometer may be employed. 

A chronometer is simply a nicely constructed watch. To 
guard as far as possible against the irregularities that would 
arise from change of temperature, the balance wheel is com- 
pensated, the compensation being made in such manner as 
to neutralize the irregularities, not only of the balance 
wheel itself, but of the hair-spring. Particular attention is 
given to the escapement and also to the winding arrange- 
ment. 

To secure uniformity of rate it is necessary that the 
chronometer should remain, as nearly as possible, in a fixed 
position. For this reason the instrument is suspended by 
a sort of universal joint, and in such manner that its face 
shall always be horizontal. 



110 ASTRONOMY. 



Error of a Clock, or Chronometer. 

83. There are several methods of finding the error of a 
clock or chronometer with respect to mean time. 

1°. By a transit of the sun. In this method we note 
the reading of the clock, or chronometer, at the instant 
when the advancing limb or edge of the sun crosses the 
meridian, and also when the following limb crosses it ; the 
half sum of these is the clock reading at apparent noon, 
from which we have at once the apparent error of the time- 
piece ; this result corrected for the equation of time is the 
error required. 

2°. By measuring the altitude of the sun. In 
this method we are supposed to know the latitude of the 
place and the declination of the sun. We measure the alti- 
tude of the sun's lower limb, and at the same time we note 
the reading of the chronometer. This altitude, after being 
corrected for refraction, semi-diameter, and parallax, gives 
the true altitude of the sun's centre. Subtracting the alti- 
tude of the sun's centre from 90°, we have the side ZS of 
the astronomical triangle (Art. 7G) ; subtracting the lati- 
tude of the place from 90°, we have the side PZ ; and sub- 
tracting the sun's declination from 90° we have the side PS. 
We may therefore compute the hour angle ZPS, which 
gives the apparent time at the instant of observation ; from 
this we can find the corresponding mean time, and conse- 
quently the error of the chronometer. 

By finding the error of the chronometer at two instants 
sufficiently remote from each other, we can find the rate 
(Art. 18). 

The error of a clock or watch may also be determined by means of 
observations made upon a star either when on or off the meridian. 
When either the sun, or a star, is observed off the meridian, it is 
better to make two observations, one when the body is east and the 
other when it is west of the meridian, and these should be made at 
nearly equal times before and after culmination. 



THE EARTH. HI 



Relation of Longitude and Time. 

84. The longitude of a place is the angular distance of 
the meridian of that place from some fixed meridian. It 
is reckoned from the fixed meridian toward the west, and 
may be expressed either in units of angular measure or in 
units of time. Longitude is generally reckoned from the 
meridian of Greenwich, England, but it may be reckoned 
from any other meridian; thus, in the United States longi- 
tude is often reckoned from the meridian of Washington. 
To avoid confusion we shall always regard the meridian of 
Greenwich as the fixed or prime meridian. 

It lias been stated already that we may either suppose the earth to 
revolve from west to east carrying the meridians of different places 
with it, or that we may conceive the earth to be at rest and the 
heavens to revolve with an equal angular velocity from east to west, 
inasmuch as the apparent motions of the heavenly bodies will be the 
same in either case. In showing the relation of longitude and time 
the latter idea will be adopted, not only because it is simpler, but be- 
cause the motions to be considered will then correspond to the direc- 
tion in which longitude is reckoned. 

Let us first consider the apparent motion of the vernal equinox, 
calling the time at which it is on the meridian of any place sidereal 
noon. Setting out from the meridian of Greenwich the equinox 
travels westward at the rate of 15° in a sidereal hour ; hence, when it 
is sidereal noon at a place on any other meridian the sidereal time at 
Greenwich, in, hours, is equal to the number of degrees in the longi- 
tude of the place divided by 15, that is, the longitude of any place, 
expressed in time, is the difference between the sidereal time at the 
place, and at Greenwich. 

For example, the longitude of New York is 74°, and consequently 
the time required for the equinox to travel from the meridian of 
Greenwich to that of New York is -f § of an hour, or 4 hours 56 min- 
utes ; hence, when it is sidereal noon in New York, the sidereal time 
at Green wuch is 4 hours 56 minutes ; when the sidereal time at New 
York is 1 hour, the sidereal time at Greenwich is 5 hours 56 minutes ; 
when the sidereal time at New York is 2 hours the sidereal time at 
Greenwich is 6 hours 56 minutes, and so on. The longitude of New 
York, expressed in time at the rate of 15° to the hour, is, therefore, 



112 ASTRONOMY. 

equal to the difference of the local sidereal times at New York and at 
Greenwich. 

Again, let us consider the apparent motion of the mean 
sun. Setting out from Greenwich the mean sun travels 
uniformly toward the west, returning to that meridian at 
the end of 24 mean solar hours ; hence, it travels westward 
with respect to any meridian at the rate of 15° in a mean 
solar hour. Consequently, wdien it is mean noon at a place 
on any other meridian the mean solar time at Greenwich, 
in hours, is equal to the rfumber of degrees in the longitude 
of the place divided by 15, that is, the longitude of a place, 
expressed in time, is equal to the difference between the 
mean solar time at the place, and at Greenwich. 

From what precedes, we infer that the difference between 
the longitudes of any two places, expressed in time, is equal to 
the difference of the local times at the two places at the same 
instant, and this whether the time considered is sidereal, or 
mean solar. Conversely, the difference of local time at any 
two places is equal to their difference of longitude expressed 
in time. 

The Chronograph. 

85. A chronograph is a contrivance for recording the 
times of astronomical observations by means of the electric 
current. 

The recording part of the apparatus consists of a revolv- 
ing cylinder and a suitable recording pen. The cylin- 
der, which carries a sheet of paper wrapped around it, is 
made to revolve on its axis at the rate of one turn per min- 
ute, and at the same time the recording pen is made to ad- 
vance in the direction of the axis of the cylinder at the rate 
of about £ of an inch per minute. The pen is moved to and 
from the revolving paper by means of an electro-magnet 
and a counteracting spring. When the electric circuit is 
completed the pen is pressed against the paper and a signal 



THE EARTH. 113 

is recorded ; when the circuit is broken the pen is thrown 
back by the spring. 

The recording apparatus is connected with the clock in 
such a manner that the circuit is completed, and a signal 
recorded, at each beat of the pendulum ; it is also con- 
nected with a key by means of which the circuit may be 
completed, and a signal recorded, at the pleasure of the ob- 
server. By a simple mechanical arrangement the pen is 
slightly displaced at each beat of the pendulum, so that a 
peculiar form is given to the clock-signals, which distin- 
guishes them from those made by means of the key. An 
arrangement is often made by which the record of the last 
second of each minute is omitted; this facilitates the opera- 
tion of determining the time that corresponds to any signal. 

When the instrument is in use the clock-signals are regis- 
tered automatically, and it only remains to connect them 
with the reading of the clock ; this is done by writing the 
clock time at the beginning of any minute over the corre- 
sponding signal on the revolving paper. In registering the 
transit of a star the observer holds the key in his hand, 
closing it briskly when the star crosses a line of the reticle. 
The time corresponding to each of these signals can be de- 
termined by its distance from the adjacent clock-signals. 

It is to be noted that the recording apparatus need not be near the 
observer ; it may even be hundreds of miles from the place of obser- 
vation. 

Methods of Determining Longitude. 

86. The operation of finding the difference of longitude 
of two places consists in finding the difference of the local 
times of the places at any given instant (Art. 84). The fol- 
lowing are some of the methods employed : 

1°. By chronometer. In this method the observer is 
provided with a chronometer whose error with respect to 
Greenwich time at a given epoch, and whose rate are 



114 ASTRONOMY. 

known. From these data the observer can compute the 
local Greenwich time at any instant. By one of the 
methods explained In Art. 83 he can determine his local 
time at the same instant. The difference between these 
local times is the required longitude. 

This is the method which is generally used at sea, and by travel- 
ers. It is somewhat uncertain on account of the liability of a chro- 
nometer to change its rate. The accuracy of the determination may 
be increased by using two or more chronometers. 

2°. By signals. This method requires two observers, 
each provided with a chronometer, whose error and rate are 
known. The observers are stationed at the places whose 
difference of longitude is to be determined, and at a time 
agreed upon a signal is made which can be seen from both 
stations. The chronometer time of the signal, which may 
be a flash of gunpowder, the bursting of a rocket, or some- 
thing of the kind, is noted by both observers, and each de- 
termines his corresponding local time. The difference of 
these local times is the difference of longitude* between the 
two stations. 

3°. By the eclipses of Jupiter's satellites. The 
eclipses of Jupiter's satellites, as we shall see hereafter, are 
of frequent occurrence ; the times at which they take place 
are computed in advance and laid down in the Nautical 
Almanac. If an observer knows his longitude approxi- 
mately, he can find the approximate local time at which an 
eclipse is to be looked for, and when it happens he has only 
to note the reading of his chronometer ; from this he can 
find the correct local time of the phenomenon. The differ- 
ence between the local time thus found and the correspond- 
ing Greenwich time, taken from the almanac, is the longi- 
tude of the place of observation. 

4°. By lunar distances. It will be seen hereafter that 
the moon moves eastward among the stars at the rate of a 
little more than half a degree per hour; it is therefore con- 



THE EARTH. 115 

tmually approaching those stars that lie to the east, and 
continually receding from those that lie to the west. The 
angular distances between the moon and certain bright 
stars as seen from the centre of the earth are computed for 
every three hours and laid down in the Nautical Almanac. 

In order to find the longitude of a place the observer de- 
termines, by observation and computation, the geocentric 
angle subtended by the moon and a suitable star at any in- 
stant ; he then finds from data given in the almanac the 
Greenwich time at which the bodies subtend this angle. 
The difference between the local time of observation and 
the corresponding Greenwich time is the required longitude. 

5°. By the electric telegraph. When two places are 
in telegraphic communication the best method of determin- 
ing their difference of longitude is by means of electric sig- 
nals. This method requires two observers, each provided 
with a transit instrument, a clock or chronometer, and a 
chronograph. The error and rate of each clock having 
been carefully determined, both clocks are connected with 
one of the chronographs and allowed to record their beats 
for a few minutes ; both clocks are then connected with the 
other chronograph and again allowed to record their beats 
for an equal time. From these records and the known 
errors of the clocks at the corresponding times, the differ- 
ence between the local times at the two stations can be de- 
duced and this is the required longitude. 

A single set of chronographic observations would be suf- 
ficient to determine the difference of local times, were it 
not for the fact that a certain period of time is required for 
the electric current to pass from one station to the other. 
In finding the difference of local times we have to subtract 
the time at the western station from that at the eastern 
station. But when both clocks are connected with the 
eastern chronograph, the recorded time of the western 
clock will be too great by the period required for electricity 
to travel over the distance between the stations, and conse- 



116 ASTKONOMY. 

quently the recorded difference of local times will be too 
small by that amount. Again, when the clocks are con- 
nected with the western chronograph the recorded time of 
the eastern clock will be too great by the time required for 
electricity to travel over the distance between the stations, 
and consequently the recorded difference of local times will 
be too great by that amount. Hence, if we determine the 
differences of the local times as recorded upon both chrono- 
graphs, the half sum of these differences will be the required 
difference of times, corrected for the time required for elec- 
tricity to travel from station to station. 

As an illustration, let E be an eastern and W a western 
observer, and suppose that it requires 0.4 second for the 
current to pass from one to the other. At 12 o'clock, E 
sends a signal to W which is received, say at 11 hours 
46 minutes 42.9 seconds, giving an apparent difference of 
local times equal to 13 minutes 17.1 seconds ; again at 12 
o'clock, W sends a signal which is received by E at 12 hours 
13 minutes 17.9 seconds, giving an apparent difference of 
local times equal to 13 minutes 17.9 seconds. The half 
sum of these differences, which is 13 minutes 17.5 seconds, 
is the required difference of longitude. 



V. THE MOON. 

The Moon's Actual Path in Space. 

87. The moon is a satellite of the earth, revolving 
around it and at the same time accompanying it in its 
annual journey around the sun. 

During the earth's revolution around the sun the plane 
of the lunar orbit is carried along with it, and because this 
plane is always inclined to the earth's orbit it follows that 
the moon's real path in space is a species of flattened spiral 
winding once around the earth's orbit in each revolution of 
the moon, but never returning into itself. 

In what follows we shall only consider the moon's motion 
with respect to the earth, that is, we shall disregard that 
part of her motion which is due to the common revolution 
of the earth and moon around the sun. 

Definitions and Explanations. 

88. The moon's orbit is an ellipse, one focus of which 
is at the centre of the earth, or, more strictly speaking, at 
the common centre of gravity of the earth and the moon, a 
point that is always within the body of the earth. She 
moves along this orbit in such a manner that her radius- 
vector, that is, the line from the earth to the moon, 
sweeps over equal areas in equal times. Her mo- 
tion is from west to east, and her velocity is such that she 
travels from any given star completely around the heavens 
back to the same star in about 27^ days ; this time is called 
her sidereal period. 

The point of the moon's orbit which is nearest the earth 
is called perigee, that which is farthest from the earth is 



118 



ASTRONOMY. 



called apogee, and the line joining them is called the line 
of apsides ; in consequence of the law of equable descrip- 
tion of areas the moon's angular velocity is a maximum at 
perigee and a minimum at apogee. 

The plane of the moon's orbit is inclined to that of the 
ecliptic in an angle that is slightly variable, but whose mean 
value is 5° 8' 30" ; the points in which the orbit intersects 
the plane of the ecliptic are called nodes, and the line join- 
ing them is called the line of nodes. The point at which 
the moon passes from the south to the north side of the 
ecliptic is the ascending node, and the point at which 
she passes from the north to the south side of the ecliptic 
is the descending node. 



Mean Distance and Horizontal Parallax. 

89. The moon's mean distance from the earth is a little 
less than 239,000 miles, and the corresponding value of her 
equatorial horizontal parallax is about 57'. The excentri- 
city of the orbit is variable, its mean value being 0.055 ; 
hence, the moon's average distance when in perigee is about 
226,000 miles, and when in apogee about 252,000 miles. 
Of course the horizontal parallax varies with the varying 
distance of the moon. The distance and corresponding 
value of the parallax may be found by the following 
method. 

y Explanation. The curve PQP'E repre- 

\,f sents a meridian section of the earth; EQ, 

^-<-'' the equator ; A, B, two stations on the me- 

,--'' S/ ridian ; and M, the apparent place of the 

--'' y' / moon when on the meridian. • 



The geocentric latitudes of A and 
B being given, the radii CA and CB 
are known from the properties of an 
ellipse, and consequently the angle 
ACB; hence, the chord AB and the 
angles CAB, CBA can be comput?d. 
The supplement of the zenith dis- 




Fig. 49. Method of finding Dis- 
tance of Moon. 



THE MOON. 119 

tance ZAM, diminished by CAB, gives BAM ; and in like manner we 
have MBA ; hence, the angle AMB and the distance AM can be found. 
Knowing CA, AM, and the angle CAM, we can compute CM, which is 
the moon's distance, and CMA, which is the parallax corresponding to 
the apparent zenith distance ZAM. From these elements we can easily 
deduce the horizontal parallax for the radius CA, and thence the hori- 
zontal parallax for the equatorial radius, that is, the moon's equatorial 
horizontal parallax corresponding to the distance CM. 

The elements given in this and the preceding articles are subject to 
the disturbing influence of the sun and planets, which act to draw the 
moon slowly but continuously from its normal orbit. We may, how- 
ever, continue to regard her orbit as elliptical if we suppose the ellipse 
to vary slightly at each instant both in its position and in its form. A 
complete discussion of this subject is beyond the scope of the present 
work, but some of the changes that take place will be pointed out in 
the following article. 



Irregularities in the Moon's Motion. 

90. The following are some of the most important of the 
changes that take place in the lunar orbit in consequence 
of the disturbing influence of the sun, and the smaller 
perturbations due to the action of the planets. 

1°. The inclination of the plane of the lunar orbit is 
subject to an alternate increase and decrease ;, its least value 
is about 4° 57', and its greatest value is about 5° 20', giving 
for the mean or average inclination about 5° 8' 30''. 

This change is equivalent to a rocking or vibratory motion of the 
orbital plane about the line of nodes. 

2°. The line of nodes has a retrograde motion in the 
plane of the ecliptic ; that is, a motion from east to west, 
by virtue of which it performs a complete revolution with 
respect to the stars in about 18.6 years. 

This change is equivalent to a revolution of the plane of the moon's 
orbit around an axis passing through the centre of the earth, and per- 
pendicular to the plane of the ecliptic ; that is, making an angle with 
the plane of the orbit whose average value is 84° 51 / 30". 



120 ASTRONOMY. 

3°. The line of apsides, which is the same thing as 
the transverse axis of the orbit, has a direct motion by virtue 
of which it performs a complete revolution from west to 
east in a little less than 9 years. 

This change is equivalent to a revolution of the orbit in its own 
plane around an axis passing through the centre of the earth, and 
perpendicular to the plane of the orbit. 

4°. The excentricity of the orbit is subject to an alter- 
nate increase and diminution, either of which may amount 
to more than \ ofHhe mean value of the entire excentricity, 
which is about 0.055. The minimum value of the excen- 
tricity may therefore become less than .044, and its maxi- 
mum value may become greater than .066. 

This change produces a corresponding change in the difference 
between the apogean and the perigean distances of the moon, the 
difference being about 21,000 miles when the excentricity is a mini- 
mum, and about 31,000 miles when the excentricity is a maximum. 

5°. The mean distance, which is the same thing as the 
semi-transverse axis of the orbit, is subject to a secular 
change; that is, a change that extends through an im- 
mensely long period. At present the mean distance is 
diminishing. 

These changes are taking place simultaneously, and all of them 
are more or less irregular ; hence, the operation of computing the 
moon's place in the heavens is extremely tedious. The place of the 
moon, determined by tables constructed for the purpose, is laid down in 
the Nautical Almanac for every hour of the day throughout the year. 

Angular Diameter of the Moon. 

91. The angular diameter of the moon varies in- 
versely as her distance from the observer ; when she is at 
her mean distance, her angular diameter as seen from the 
centre of the earth is 31' 7". 



THE MOOK. 121 

One-half of the angular diameter of the moon is called 
the moon's apparent semi-diameter. 

Because the moon is farther from the centre of the earth than she 
is from any point on the surface from which the moon is visible, the 
apparent semi-diameter of the moon when seen from the surface is 
greater than it would be if seen from the centre. This excess, which is 
called the augmentation of the moon's semi-diameter, obviously increases 
as she approaches the zenith of the observer. The mean distance of 
the moon from the centre of the earth is a little more than 60 times 
the terrestrial radius ; hence, her mean distance from that point of 
the surface which lies directly between the centres of the earth and 
moon is a little more than 59 terrestrial radii. At this point, there- 
fore, the augmentation of the moon's semi-diameter is about z \ of its 
entire value ; that is, it amounts to nearly 16". 

Magnitude, Mass, and Density of the Moon. 

92. The semi-diameter of the moon in miles is found 
by multiplying her distance from the earth by the sine of 
her apparent semi-diameter. In this way we find that 
her serni-diameter is equal to 1080 miles, and consequently 
her diameter is 2160 miles. From this we infer that the 
volume of the moon is about -g^th that of the earth. 

The mass of the moon, as found by the methods of phy- 
sical astronomy, is about -g^th that of the earth. The den- 
sity of the moon is therefore about -fths that of the earth, 
or about 3-|- times that of water. 

Synodic Period.— Phases. 

93. The moon's synodic period, which is the same as 
a lunar month, is the interval between two consecutive 
conjunctions of the sun and moon. In consequence of 
irregularities in the motions of both of these bodies, the 
length of the synodic period is somewhat variable ; its 
average length, however, is found to be about 29.53 days. 
For the ordinary purposes of description its length is taken 
as 29| days. 



122 ASTEONOMY. 

During a lunar month the bright part of the moon as- 
sumes a succession of different forms called phases ; these 
are due to a continual change in the position of the ob- 
server with respect to the sun and the moon. 

The illuminated half of the moon is turned toward the 
sun and the line that separates it from the unilluminated 
part is called the terminator. The plane of the termina- 
tor, except at conjunction and opposition, is oblique to the 
observer's line of vision ; hence, its projection on the moon's 
disk is elliptical. The bright part of the moon's disk is 
therefore bounded on one side by a semicircle, and on the 
other side by a semi-ellipse. 



Fig. 50. Phases of the Moon. 

Explanation. E is the position of the earth ; ES' is the direction from E to the 
snn ; M0Q.S is the moon's orbit, supposed to lie in the plane of the ecliptic ; M, N, 
0, P, etc., are the representations of the moon's phases when her elongations from 
the sun are 0°, 45°, 90°, 135°, etc. ; and the arrow- heads show the direction of the 
moon's motion. 

The different phases of the moon and their order of suc- 
cession are shown in Fig. 50. When the moon is at M, 
that is, when she is in conjunction with the sun, her illumi- 
nated face is turned away from the earth, and is therefore 
invisible ; the moon is then said to be new. After passing 
M a portion of the illuminated face comes into view, and 
this portion continues to increase until she reaches Q, when 
her entire illuminated face is turned toward the earth ; the 



THE MOON. 123 

moon is then said to be fall. After passing Q the visible 
portion of her illuminated face begins to diminish, and this 
diminution goes on until she returns to M, when she again 
becomes invisible. When the moon is at she is said to be 
in her first quarter, and when at S she is said to be in 
her third quarter. 

Between M and 0, and between S and M, the moon's 
phase as shown at X and T is said to be crescent ; be- 
tween and Q, and between Q and S, her phase as shown 
at P and R is said to be gibbous ; at and at S her phase 
is said to be dichotomous. 

In all its changing forms the circular portion of the 
moon's apparent outline is turned toward the sun ; hence, 
from new moon to full moon the western limb is circular, and 
from full moon to new moon the eastern limb is circular. 

The earth, as seen from the moon, goes through a suc- 
cession of phases which are always complementary to those 
of the moon as seen from the earth, that is, when the moon 
has a crescent phase the earth has a gibbous phase, and the 
reverse. 

For a few days before and after new moon the dark part 
of the moon is faintly visible ; this is due to light twice 
reflected. The earth being nearly full at that time, as seen 
from the moon, reflects a sufficient amount of sunlight to 
render the entire disk of the moon faintly visible to a ter- 
restrial observer. 

It is noticeable at this time that the semicircle that 
bounds the bright limb appears perceptibly larger than that 
which bounds the dark limb ; this is an optical delusion due 
to irradiation. It is an established principle of optics that 
a bright circular disk appears larger than a dark one of the 
same size ; hence, the phenomenon in question. 

Other Lunar Periods. 

94. Besides the sidereal and the synodic periods already 
referred to, the moon has two other periods frequently used 



124 ASTRONOMY. 

by astronomers, the nodical and the anomalistic periods. 
The nodical period is the interval between two successive 
returns of the moon to the ascending node ; and the anom- 
alistic period is the interval between two successive re- 
turns of the moon to perigee. 

Because the ascending node has a retrograde motion, the 
arc passed over by the moon in a nodical revolution is less 
than a complete circumference by the arc that is passed over 
by the node in that time ; hence, the nodical period is less 
than the sidereal period. Again, because the perigee has a 
direct motion, the arc passed over by the moon in an anom- 
alistic period is greater than a complete circumference by 
the arc passed over by the perigee in the same time ; hence, 
the anomalistic period is greater than the sidereal period. 

For convenience of reference the average values of four 
principal lunar periods are given below : 



Sidereal period 27.32 

Synodical period 29.53 days. 

Nodical period 27.21 days. 

Anomalistic period 27.55 days. 

Rotation of the Moon. 

95. It is a matter of common observation that we always 
see very nearly the same face of the moon ; that this may 
be the case, the moon must revolve around an axis in the 
same time that she makes a revolution in her orbit, and, 
furthermore, her axis of revolution must be nearly perpen- 
dicular to the plane of her orbit. 

More accurate observations show that the plane of the 
moon's equator intersects the plane of her orbit in a line 
that is parallel to the line of nodes. A plane passing 
through this line and parallel to the ecliptic lies between 
her equator and her orbit, the former making an angle of 
about 11° on one side, and the latter an angle of about 5° 
on the other side, as shown in Fig. 51 ; hence, the plane of 




THE MOOS. 125 

the moon's equator makes an angle of 6£° with the plane of 
her orbit. 

Explanation. The plane of the 
pamper is supposed to be perpendicu- 
lar to the ecliptic and to the moon's 
orbit. N is the projection of the line 
of nodes ; NC is the projection of the 
ecliptic ; NO is the projection of the 
moon's orbit ; MQ is the projection Fig. 51. Position of the Moon's Equator. 
of the moon's equator; and MB is 

parallel to NC. The angle QMB is equal to li° ; the angle OMB is equal to 5° ; and 
the angle QMO is 6h°. MA, perpendicular to MQ, is the axis of the moon, making 
an angle of l^ with the axis of the ecliptic. 

The moon's axis of rotation makes an angle of 1-J with the axis of 
the ecliptic, and is always perpendicular to the line of nodes ; hence 
the axis of the moon has a retrograde motion by virtue of which it de- 
scribes a very acute conical surface in 18.6 years, which is the time 
required for the line of nodes to complete an entire revolution. This 
gyratory motion is similar to that of the earth's axis as explained in 
Art. 73. 



The Moon's Librations. 

96. In consequence of the moon's irregular motion her 
visible face is not always exactly the same ; it is subject to 
slight periodical changes, such as would be produced if the 
moon were made to rock back and forth around certain lines 
as axes. These oscillatory motions, which are only apparent, 
are called librations. 

The moon has two principal librations, one with respect 
to an axis perpendicular to the plane of the orbit, and the 
other with respect to an axis in that plane ; the former is 
called libration in longitude, and the latter libration 
in latitude. 

1°. Libration in longitude. This libration is due to 
the fact that the moon revolves uniformly around her axis 
whilst her angular velocity with respect to the earth is 
variable. Because the moon's radius-vector sweeps over 
equal areas in equal times, she will occupy the same time in 



126 



ASTRONOMY. 



passing from perigee to apogee as in passing from apogee to 
perigee ; hence, so far as this libration is concerned, the 
visible face of the moon at apogee will be the same as at 
perigee. In setting out from perigee her orbital angular 
Telocity is greater than her angular velocity of rotation ; 
we therefore see more of her western and less of her eastern 
face than we do at perigee. The additional portion that 
thus becomes visible goes on increasing during the first 
quarter of the anomalistic period, and then it decreases 
during the second quarter, at the end of which time the 
visible portion, as we have said above, is the same as at 
perigee. But, in setting out from apogee the circum- 
stances of motion are reversed, and we see more of her 
eastern and less of her western face than we do at apogee. 
This additional portion goes on increasing during the third 
quarter of the anomalistic revolution, and then it dimin- 
ishes during the fourth quarter, at the end of which time 
the moon presents to us the same face as at apogee. 

The entire cycle of this libration is equal to the anoma- 
listic period of the moon, during which the appearances 
presented are the same as the ugh the moon had been 

slightly rocked back and 
'nTv forth around an axis per- 

pendicular to the plane of 
her orbit. 



Explanation. M and P are the 
position? of tbe moon at perigee and 
apogee ; N and Q, are her positions at 
the end of the first aud third quarters 
of her anomalistic revolution ; ah is 
the plane that determines the visible 
portion of her surface when at M and 
P ; and cd ar.d ef ■ are the planes that 
limit her visible surface when at N 
and Q. 




Fig. 52. The Moon's Libration in Longitude. 



2°. Libration in latitude. This libration is due to 
the fact that the axis of the moon is inclined to the plane 



THE MOOK. 127 

of her orbit. When the moon is at either node the plane 
that limits her visible surface passes through her axis, and 
consequently the visible surface extends from pole to pole. 
When her angular distance from either node is 90°, the 
plane that limits her visible surface makes an angle of C^° 
with the axis ; if at this time she is south of the ecliptic, 
the visible surface extends 6-§-° beyond the north pole, but 
if she is north of the ecliptic the visible surface extends 
6-}° beyond the south pole. 

The entire cycle of this libration is equal to the nodical 
period of the moon, during which the appearances pre- 
sented are the same as though the moon had been slightly 
rocked back and forth around the line of nodes of the 
moon's orbit. 

ft , 

F "** «0 

~<g 

Fig. 53. The Moon's Libration in Latitude. 

Explanation. The plane of the paper is perpendicular to the line of nodes 
which is projected at E, the place of the earth ; EC is the projection of the ecliptic ; 
M and Q, are the positions of the moon when 90° from either node ; NS is the axis 
of the moon ; and ab and cd are the planes that limit the visible part of the moon's 
surface when at M and Q,. 

In this connection we may mention a change that takes place in 
the visible face of the moon between the times of rising and setting. 
This change, which is sometimes called the diurnal libration, is sim- 
ply parallactic. It is due to the fact that the centre of the moon's 
visible face as seen from the surface of the earth is not the same that 
it would be if seen from the centre. As a consequence, a little more 
of her western limb, or edge, is visible at the time of rising and a little 
more of her eastern limb, or edge, at the time of setting than can be 
seen w 7 hen she is on the meridian. 

The combined effect of the moon's librations enables us 
at one time or another to see nearly -fths of the moon's 
entire surface. 



128 ASTRONOMY. 

Variation of the Moon's Meridian Altitude. 

97. It is a matter of common observation that the alti- 
tude of the moon at her upper culmination is widely varia- 
ble. This variation is caused by the continual change in 
the moon's declination. 

The moon's meridian altitude, as observed at any place, is 
equal to the co-latitude of the place increased by the moon's 
declinatiofi, due regard being paid to the sign of the latter 
element (Art. 16). Now, the moon's declination depends 
not only upon her place in her orbit, but also on the posi- 
tion of her orbit with respect to the ecliptic. The variation 
in the moon's declination is greatest when the ascending 
node of her orbit is at the vernal equinox, and least when 
the ascending node is at the autumnal equinox. In the 
former case the declination varies in a nodical period from 
-4-28^-° to — 28-§-° ; in the latter case it varies from + 18-|- 
to — 18J° in the same time. 

For a place whose latitude is 40° N. the greatest meridian altitude 
of the moon in any month is 78-| c , and the least meridian altitude 

is 22|-°. 

Ou the day that the moon has the greatest meridian alti- 
tude in any month she is said to run high, and on the day 
that her meridian altitude is least she is said to run low. 

The full moon, being nearly opposite to the sun in the 
heavens, will be north of the equinoctial when the sun is 
south of it, and south of the equinoctial when the sun is 
north of it. Hence, in winter the full moon tends to run 
high, and in summer to run low. We therefore have the 
greatest amount of moonlight in the long nights of winter, 
and the least amount in the short nights of summer. 

The Harvest Moon. 

98. On account of the eastward motion of the moon with 
respect to the sun, her time of rising is continually retarded ; 



THE MOON. 129 

her daily retardation, which is variable, amounts on an 
average to about 49 minutes. The retardation is least when 
she is in that part of her orbit which is least inclined to the 
horizon, for in that case her daily advance carries her but 
little below the horizon, and consequently the change in the 
time of her rising is correspondingly small. The retarda- 
tion in the time of rising of the full moon that falls near 
the time of the autumnal equinox is generally less than 
half an hour for several days in succession. In England, 
on account of increased latitude, the phenomenon in ques- 
tion is more strongly marked than it is in the United 
States ; and because it occurs about the time of their har- 
vest, the September moon has been called the harvest 
moon. 



Character of the Moon's Surface. 

99. To the naked eye the surface of the moon presents a 
mottled appearance such as we might suppose it would offer 
if it were made up of land and water. When examined 
with a good telescope, it is found that the brighter portions 
are mountains and the darker portions slightly undulating 
plains, but no trace of water is anywhere to be seen. 

The mottled appearance of the moon's surface, which is 
more strongly marked along the terminator, is shown in 
Fig. 54. 

100. Taken as a whole, the visible surface of the moon 
is exceedingly irregular, more than half of it being made 
up of rugged mountain masses variously grouped and ar- 
ranged. Occasionally we see an isolated peak casting its 
black shadow on the neighboring plain, and sometimes we 
meet with a continuous mountain range interrupted by deep 
and rocky gorges ; but for the most part the grouping is so 
irregular as to defy all attempts at description. The ar- 
rangement of the mountain systems is shown in Fig. 55. 



130 



ASTROHOMY. 



101. The roughness of a large portion of the lunar sur- 
face is much greater than that of our most mountainous 
regions. The ridges everywhere show an abruptness of de^ 
clivity and a sharpness of outline which seem to preclude 
all idea of the existence of those atmospheric agencies 
which are ever at work smoothing down and rounding off 
irregularities on the surface of the earth. The rugged char 
acter of the moon's surface is shown in Fig. 5&. 




Fig. 54. Telescopic Appearance of the Moon. From a photograph toy Prof. 
Henry Draper. 



102. A striking feature in the lunar topography is the 
tendency of its mountain forms to a circular arrangement. 
The number of crater-like objects that are shown by a good 



THE MOON. 



131 



telescope amounts to many thousands ; in some parts of the 
moon they are crowded together like the cells of a honey- 
comb. The larger formations of this class consist of circu- 
lar ridges enclosing large plains ; the enclosed areas are 
called bulwark plains, and their surrounding ridges are 
named ring mountains. In almost every case of this kind 
the inner slope of the ring mountain is steeper than the 

N 




Fig. 55. "Distribution of Mountains and Plains. 
Model of the Moon by Nasmyth. 



From a photograph of a 



Explanation. The top of Fig. 55 corresponds to the northern limb of the 
moon and the left-hand side to the eastern limb. The prominent mountain range, 
originating near a large crater-like formation in the north-eastern quadrant and 
running in a north-westerly direction, is called the Apennines ; the crater itself is 
named Copernicus. The shorter chain, north of and nearly perpendicular to the 
Apennine range, but separated from it by a wide gap, is called the Alps ; the Alpine 
chain terminates toward the nortb-east in a large crater named Plato. The south- 
ern part of the figure sbows little else than a confused mass of compacted cliffs, 
ridges, and volcanic craters. 



132 



ASTRONOMY. 



outer one. In some instances the ring mountain is made 
up of irregular concentric ranges; such a formation is 
shown in Fig. 57. 




Fig. 56. Enlarged View of the Alpine Region. 



Explanation. The large crater toward the upper part of the figure is Plato ; 
the character of its bounding rim is shown by the shadows cast on the floor of the 
enclosed area. The remarkable cleft, traversing the middle part of the range, is 
the great valley of the Alps • it is more than 80 miles long, from 3| to 5J miles wide, 
and more than 2 miles in depth at its deepest part. The lower part of the figure 
represents a part of the great plain, called Mare Imbrium. 

The smaller circular formations have every appearance of 
being true volcanic craters. In some of these the central 
depression consists of a deep cavity, apparently terminating 
in a point ; in others the central depression terminates in a 
flat plain lying below the general level of the moon's sur- 
face ; not infrequently there is a conical peak rising from 
the middle of this floor of the crater. 



THE MOCTN". 



133 




Fig. 57. Copernicus. 

Explanation. Pig. 57 represents the ring mountain Copernicus. It is com- 
posed of terraces and ridges separated by deep ravines. The diameter of the en- 
closed area is more than 50 miles. Rising from the enclosed plain are 5 or 6 peaks, 
one of which is nearly half a mile in height. 

103. In some parts of the lunar surface vast cracks or 
fissures exist, which may be traced to a considerable distance 
from their apparent origin. Such a system of cracks is 
shown in Fig. 58, the principal ones seeming to start from 
a small crater, near the large ring mountain, or crater, 
Triesnecker, situated not far from the centre of the lunar 
disk. 




Fissures near Triesnecker, 



134 



ASTRONOMY. 



Another example of these cracks, or faults, is shown in 
Fig. 59, which represents an ideal view of the peak named 
Pico, situated nearly south of Plato in the Mare Imbrium. 




Explanation. Fig. 59 is an ideal view of a lunar mountain peak. In the fore- 
ground we see not only the crack, or fissure, referred to, but also a number of 
minute craters. 

104. At the time of full moon several systems of bright 
streaks are seen, each system diverging from a central 
crater. Of these the most remarkable set seems to originate 
in Tycho, the most prominent volcanic centre in the south- 
ern hemisphere of the moon. Some of these streaks extend 
to a distance of more than 1,700 miles. They appear to 
coincide with the general level of the moon's surface, and 
in many cases they pass over mountains and across ravines 
without any apparent interruption. Proctor says: "It 
seems clear that, as Nasmyth has illustrated by experiment, 
they belong to that stage of the moon's history when her still 
hot and plastic crust parted with its heat more rapidly than 
the nucleus of the planet, and so, contracting more quickly, 
was rent by the resistance of the internal matter, which, still 
hot and molten, flowed into the rents, and spreading, formed 
the long broad streaks of brighter surface." 



VI. THE SUN AND PLANETS. 

The Sun's Place in the System. 

105. The sun is the principal body of the solar system, 
and as such it not only controls and regulates the motions 
of all the others, but it is to them their chief source of 
light, heat, and physical energy. His volume is more than 
600 times the volume of all the planets taken together, and 
his mass is more than 700 . times their aggregate mass. 
Among the fixed stars he is a peer, but in the solar system 
he is a ruler. 

Orbit of the Earth. The Sun's Apparent Orbit. 

106. It has already been stated (Art. 11) that the sun's 
apparent annual motion from west to east among the stars 
is due to the actual motion of the earth, which revolves 
around the sun in an orbit whose plane passes through the 
centres of the two bodies and retains a sensibly fixed posi- 
tion with respect to the stars. 

If the line joining the centres of the earth and sun be 
indefinitely prolonged, it will meet the celestial sphere in 
two points diametrically opposite to each other. One of 
these is the heliocentric place of the earth, and the other 
is the geocentric place of the sun. Inasmuch as the line 
from the earth to the vernal equinox is parallel to the line 
from the sun to the same point, it follows that the differ- 
ence between the geocentric longitude of the sun and the 
heliocentric longitude of the earth is equal to 180°. 

The orbit of the earth is an ellipse having one of its 
foci at the centre of the sun. Its excentricity is about 



136 



ASTRONOMY. 



■g 1 ^ that is, the distance of the sun from the centre of the 
orbit is about one-sixtieth of the semi-transverse axis. The 
heliocen trie longitude of the perihelion point at the present 
time is not far from 100° 54' ; hence, the geocentric longi- 
tude of the sun when in apogee, that is, when nearest the 
earth, is about 280° 54'. 

The relation between the earth's actual orbit around the 
sun and the sun's apparent orbit around the earth is illus- 
trated in Fig. 60. 




Fig. 
Orbit. 



Diagram showing the Earth's Actual Orbit and the Sun's Apparent 



Explanation. Diagram (A) represents the real orbit of the earth : S is the sun 
at one focus ; C is the centre ; SC is the excentricity, CE being equal to 1, and SC to 
.01677 ; E is the perihelion point ; V shows the direction of the vernal equinox ; 
VSE is the heliocentric longitude of E ; W is the aphelion point ; and E" is any 
point of the orbit, its radius-vector being SE". Diagram (B) represents the appar- 
ent or relative orbit of the sun: E is the earth at one focus ; S is the place of the 
sun when in perigee ; S', his place at apogee ; V shows the direction of the vernal 
equinox ; VES, reckoned around to the left, is the geocentric longitude of S ; and 
S" is the position of the sun corresponding to E" in diagram A, the line ES" being 
always equal to SE", but lying in the opposite direction. 



107. The angle between the plane of the earth's orbit 
and that of the equinoctial, which is the same as the ob- 
liquity of the ecliptic, may be found when we know the 

sun's right ascension and declina- 
$>C *ion ; it is equal to about 23° 27'. 



Let V be the vernal equinox ; VC, an 
arc of the ecliptic ; VQ, an arc of the 
equinoctial ; S, the position of the sun ; 
VD, his right ascension ; and DS, its 




Pig. 61. Diagram. 



THE SUN AND PLANETS. . 137 

declination. In the right-angled spherical triangle VDS we know the 
right angle and the two adjacent sides ; hence, the other parts may be 
computed. The angle V is the obliquity, and the hypothenu.se VS is 
the sun's geocentric longitude. The earth's heliocentric longitude is 
found by adding 180° to VS, diminishing the sum by 360°, if neces- 
sary. 

Variation of the Earth's Distance from the Sun. 

108. The earth is in perihelion about the last of Decem- 
ber, and at that time is nearest the sun ; a half year later 
she is in aphelion, and at that time is farthest from the sun. 
Her distance from the sun increases continually from peri- 
helion to aphelion, and then it diminishes continually to 
perihelion, and so on perpetually. To compute her dis- 
tance at any time we must know her mean distance, which 
is equal to the semi-major axis of her orbit, and her angu- 
lar distance from the perihelion point, which is called the 
anomaly. 

If in Diagram (A), Fig. 60, we make the semi-major axis, CE, equal 
to 1, the excentricity equal to .01677, any radius-vector, SE", equal to 
r, and the corresponding anomaly, ESE", to <j>, we have from the polar 
equation of the ellipse 

r = .99972-K1 + .01677 cos 9), 

from which the earth's distance can be computed when we know <t>, 
which is equal to the heliocentric longitude of the earth (increased by 
360°, if necessary), diminished by that of the perihelion point. If 
.0=0, we have r=: 98323 ; if 9=180°, r=1.0l677 ; these are the peri- 
helion and the aphelion values of r. 

The values of r, as found from the preceding formula, correspond 
to the mean distance 1 ; if we multiply each by 92,500,000 miles, the 
products will be the correspondiDg values of r in miles. 

Astronomical Units. 

109. In measuring the distances and dimensions of the 
solar system (except in case of the moon) astronomers em- 
ploy, in the first instance, the earth's mean distance 
from the sun as a unit. The mean distances of all the 



138 • ASTRONOMY. 

other planets in terms of this unit are deduced from their 
periodic times (which can be found by observations that are 
comparatively, simple) by means of Kepler's third law. From 
these distances, combined with suitable observations on the 
bodies themselves, all the other distances and dimensions of 
the system are deduced. 

To convert these relative distances and dimensions into 
miles, each must be multiplied by the number of miles in 
the earth's mean distance from the sun, and any error in 
this distance will give rise to a proportionate error in each 
of the others. 

In determining the masses of the bodies of the solar sys- 
tem the mass of the earth may be taken as the unit, but 
for purposes of computation it is often more convenient to 
regard the sun's mass as the unit. 

The Different Solar Periods. 

110. A sidereal year is the time required for the earth 
to make a complete revolution around the sun. It is the 
same as the earth's periodic time, and is equal to the inter- 
val between two successive conjunctions of the sun and the 
same fixed star. Expressed in mean solar time, it is found 
to be equal to 365d. 6h. 9m. 9s., or to 365.25636 days. 

A tropical year is the interval between two successive 
returns of the sun to the vernal equinox. This is the year 
to which our calendars are adjusted, and is equal to 365d. 
5h. 48m. 46s., or to 365.2422 days. Inconsequence of the 
precession of the equinoxes the tropical year is shorter than 
the sidereal year by the time required for the sun to move 
over an arc of 50". 2, that is, by a little more than 20 
minutes. 

The anomalistic year is the interval between two suc- 
cessive returns of the earth to perihelion. In consequence 
of perturbation, the earth's perihelion has a slow motion 
from west to east amounting to about 11". 5 per year. In 
consequence of this advance of the perihelion point, the 



THE SUH AKD PLANETS. 139 

anomalistic year is longer than the sidereal year by the time 
it takes the earth to move over an arc of 11". 5. The length 
of the anomalistic year is equal to 365d. 6h. 13m. 49s., or to 
365.2596 days. 

The nodical period is the interval between two succes- 
sive returns of the sun to the ascending node of the moon's 
orbit. This period is used in treating of eclipses ; in conse- 
quence of the rapid retrogression of the moon's nodes, it 
falls considerably short of a year. Its value expressed deci- 
mally is 346.62 days. 

Periodic Times of the Planets. 

111. The periodic time of a planet may be deduced from 
the length of its synodic period in the following manner. 
If we divide 360° by the earth's periodic time the quotient 
will be the mean daily angular motion of the earth around 
the sun. Now, an inferior planet has a greater angular 
velocity than the earth, in consequence of which it gains a 
complete revolution of 360° in a synodic period;, hence, if 
we divide 360° by the number of days in the synodic period, 
the quotient will be the average daily gain of the planet, 
and this added to the earth's daily motion will give the 
planet's mean daily angular motion about the sun ; the 
number of times that this result is contained in 360° will 
be the number of days in the planet's periodic time. 

In the case of a superior planet it is the earth that gains 
360° in a synodic period ; if therefore we divide 360° by the 
number of days in the synodic period and subtract the quo- 
tient from the earth's daily motion, the difference will be 
the planet's daily motion, from which the periodic time may 
be found as before. 

From the preceding principles we may deduce a simple formula 
for the periodic time of a planet. Let e denote the earth's periodic 
time ; p, the planet's synodic period ; and t, the planet's periodic time, 



140 ASTRONOMY, 

all expressed in days. From what has been said before, we have for 
the daily motion of the planet 



360° /P ± ^\ 

± — — , which is equal to 360° I — 1 



360° 

e p ' x \pe 

dividing 360° by this result, we have, 

pe 
p±e y 

in which the upper sign is to be used for an inferior, and the lower 
sign for a superior planet. The value of p is found by actual observa- 
tion. It is to be noted that the value of p for the same planet is slightly 
variable, and to secure accuracy the mean of a great number of synodic 
periods should be taken. 

Irregularities of Planetary Motion. 

112. As seen from the sun, each of the planets has a con- 
tinuous progressive motion from west to east ; this mo- 
tion, however, is not quite uniform, being greatest when the 
planet is in perihelion and least when it is in aphelion. 
When viewed from the earth, the planetary motions are 
exceedingly irregular ; sometimes the motion of a planet is 
direct, then after a short period of apparent rest it becomes 
retrograde, and again, after another short period of appar- 
ent rest, it once more becomes direct, and so on, the cycle 
of change for each planet being equal to its synodic period. 
The arc of direct motion is always greater than that of 
retrogradation, so that the aggregate motion for long 
periods is from west to east. 

The cause of these irregularities is the motion of the 
earth, the stand-point from which the planetary motions 
are viewed ; in other words, the apparent motions of the 
planets are purely relative. According to the laws of rela- 
tive motion, a planet should appear to advance about the 
time that it is farthest from the earth, and to retrograde 
about the time that it is nearest to the earth; this is what 
is actually observed. 



THE SUN AND PLANETS. 



141 



The conditions under which the motions are either direct or retro- 
grade are shown in Fig. 62. 
c d 





Fig. 62. Illustrating the direct and retrograde motions of the planets. 



Of two planets, the one that is nearer the sun has the greater an- 
gular and also the greater linear velocity. This being premised, let 
AB, in the left-hand diagram, be an arc of the earth's orbit, and CD 
the corresponding arc of the orbit of a superior planet at about the 
time it is nearest the earth, that is, in opposition ; also let cd and ab 
be arcs on the celestial sphere. When the earth is at A the planet 
appears to be at c, and when the earth is at B the planet appears to 
be at d ; hence, whilst the earth moves over the arc AB the planet 
appears to move over the arc cd, that is, it retrogrades. Now let us 
suppose that CD is an arc of the earth's orbit and AB the correspond- 
ing arc of the orhit of an inferior planet at about the time it is nearest 
the earth, that is, in inferior conjunction. In the same manner as 
before it may be shown that whilst the earth is moving from C to D, 
the apparent motion of the planet will be from a to b, that is, retro- 
grade. Hence, when a planet is nearest the earth, whether it is a 
superior or an inferior one, its apparent motion is retrograde. 

Again in the right-hand diagram, let AB be an arc of the earth's 
orbit and CD the corresponding arc of the orbit of a superior planet 
at about the time it is farthest from the earth, that is, in conjunction. It 
may be shown as before that whilst the earth moves over the arc AB, 
the planet seems to move over the arc cd, that is, its motion is direct. 
Now let DC be an arc of the earth's orbit and AB the corresponding 
arc of the orbit of an inferior planet at about the time it is farthest 
from the earth, that is, in superior conjunction. It may be shown as 



142 ASTKONOMY. 

before that whilst the earth moves over the arc CD the planet appears 
to move from a to b, that is, its apparent motion is direct. Hence, 
when a planet, whether superior or inferior, is farthest from the earth, 
its apparent motion is direct. 

Elements of a Planet's Orbit. 

113. To trace out the path of a planet in the heavens by 
means of Kepler's laws, we must know the position and the 
form of its orbit, and also the time at which the planet is 
at some determinate point of its orbit. 

The line of nodes (Art. 51) is the line in which the plane 
of the planet's orbit cuts the plane of the ecliptic. If 
therefore we know the heliocentric longitude of the 
ascending node, we know one line in the plane of the 
planet's orbit ; if in addition we have the inclination of 
the orbit, the position of the plane of the orbit is completely 
fixed in space. 

Again, if we know the heliocentric longitude of the 
perihelion we know the direction of the major axis of the 
planet's orbit, and if in addition we know the mean dis- 
tance and the excentricity we know the shape and the 
dimensions of the orbit. 

Further, if we have the time when the planet is in peri- 
helion, called the epoch, and the periodic time of the 
planet, we have all the data required for predicting the 
place of the planet at any time whatever. 

The quantities that must be known in order to predict 
the place of a planet are called elements. The method 
of finding some of these elements has already been ex- 
plained ; the others are found by methods of practical 
astronomy, descriptions of which do not fall within the 
scope of this work. For convenience of reference, we reca- 
pitulate the elements of a planet's orbit: 

1°. The heliocentric longitude of the ascending node ; 

2°. The inclination of the plane of the orbit to that of 
the ecliptic ; 



THE SUN AND PLANETS. 143 

3°. The heliocentric longitude of the perihelion point ; 

4°. The planet's mean distance from the sun ; 

5°. The excentricity of the orbit ; 

6°. The epoch ; and 

7°. The planet's periodic time. 




Fig. 63. Kelative sizes of the sun's disk as seen from the different planets. 

The Sun's Angular Diameter. 

114. The angle subtended by the sun may be measured 
directly by means of a micrometer, or its value may be de- 



144 ASTRONOMY. 

duced from the observed time that it takes the sun's disk 
to cross the meridian of any place. When the sun is at 
his mean distance this diameter is a little more than 32' ; 
at other distances his apparent diameter varies very nearly 
as the reciprocals of those distances. When nearest the 
earth his apparent diameter is about 32' 34" ; when farthest 
from the earth it is about 31' 28". 

The sun's apparent diameter as seen from the various 
planets, including two of the planetoids, is shown in 
Fig. 63. 

When we know the sun's distance from the earth and his angular 
diameter, we can find his diameter in miles by a simple computation. 

Explanation. The figure represents A. 

a plane section of the earth and sun, the 
plane passing through the earth's centre /r ( 
E and the centre of the sun S ; EA is V_ 

tangent to the section of the sun, and SB B y S 

to the section of the earth; ES is the 
sun's distance from the earth, and AS, 
BE are radii of the sun and earth ; the Fig. 64. Diagram, 

angle AES is the apparent or angular 
semi-diameter of the sun, and ESB is the corresponding solar parallax. 

In the right-angled triangle EAS, right-angled at A, the perpen- 
dicular AS is equal to ES multiplied by the sine of the angle AES ; or 
denoting ES by D, AS by R, and the angle AES by S, we have 

R = D sin 6 (1). 

Knowing R we find the sun's diameter by multiplying it by 2. If 
the distance ES is the mean distance, and if it is taken equal to 1, we 
have the sun's actual diameter equal to twice the sine of 16'. 

From the triangle ESB, we have EB, the earth's radius, denoted by 
r, equal to D multiplied by the sine of ESB, or, denoting the latter 
angle by tt, 

?* = D sin 7r . ". . . • • • • (*). 

From (1) and (2) we have 

R : r : : sin 6 ; sin tt (3). 

That is, the ratio of the sines of the sun's apparent semi-diameter 
to the corresponding parallax of the sun is constant. 




THE SUN" AND PLANETS. 145 



The Sun's Distance and the Solar Parallax. 

115. It has been shown that the relative positions of the 
sun and planets can be found at any time, and also that 
their distances from each other can be expressed in terms 
of the earth's mean distance from the sun as a unit. Now, 
if the latter distance can be found in miles, all the other 
distances can also be found in miles ; in fact, the dimen- 
sions of the solar system are so connected that the determi- 
nation of any one (except the moon's distance from the 
earth) is equivalent to the determination of all the others. 

Many different methods of finding the sun's distance have 
been devised, all of which are more or less indirect. Among 
these, the most noted are the following : 1°, by observations 
on the transit of Venus ; 2°, by observations on Mars when 
in opposition ; and 3°, by means of the velocity of light. 

By observations on a transit of Venus. When 
Venus comes directly between the earth and the sun, as 
she does at long intervals, she may be seen as a round black 
spot traversing the sun's disk in a line which, were it not 
for the motion of the observer, would be a chord, parallel 
to the direction of the planet's motion. This phenomenon, 
which is called a transit of Venus, presents slightly dif- 
ferent aspects when seen from different points of the earth's 
surface, the chord of transit experiencing a parallactic dis- 
placement corresponding to the change of position of the 
observer. 

In the method of determining the solar parallax sug- 
gested by Halley, and commonly known as Halley's 
method, two stations are selected as far apart as possible, 
one in the northern and the other in the southern hemi- 
sphere, from each of which the whole transit can be seen. 
The times of beginning and end of the transit are observed 
at each station, and from these times, combined with the 
known rates of angular motion* of the earth and Venus, the 
lengths of the chords of transit and also the distance be- 
7 




146 ASTRONOMY. 

tween them are computed in seconds of arc. The distance 
between the chords in miles can be found from the known 
positions of the points of observation and the relative dis- 
tances of the earth and Venus from the sun. We then have 
the data for computing the angle that would be subtended 
by the earth's equatorial radius at the sun's mean distance, 
which is the solar parallax. 






Fig. 65. Solar Parallax by Halley's Method. 



Explanation. S is the sun ; V is Venus ; E is the earth ; A and D are two sta- 
tions, which, for the purpose of illustration, are taken on a line perpendicular to the 
plane of the orbit of Venus ; PQ is the chord of transit seen from D ; and RT is the 
chord of transit seen from A. 



From observations at D the chord PQ is determined in seconds of 
arc, and from observations at A the chord RT is determined in seconds 
of arc. Let SK be perpendicular to both chords ; then in the triangle 
SQK we know QK and SQ, and consequently can compute SK ; in like 
manner we can find SH ; hence, we can find SK— SH, or HK in 
seconds of arc. Again, knowing AD in miles, we can find HK also 
in miles ; for from the similar triangles ADV and HKV we have 
HK=ADx(HV-4-VA) or since HV-s-VA equals about 72-5-28, or 2f, 
we have HK=AD x 2j. If we divide HV in miles by the number of 
seconds of arc in HV, the quotient will be the number of miles re- 
quired to subtend one second of arc at the sun's actual distance, and 
from this we can easily deduce the value of the solar parallax. 

The method of determining the solar distance suggested 
by Delisle, and commonly known as Delisle's method, 
depends on the principle that any phase of a transit (as its 
beginning, for example) is not seen simultaneously at all 
points of the earth's illuminated hemisphere. 



THE SUN AND PLANETS. 147 

To understand this method, suppose the sun ana Venus to be en- 
veloped by a common tangent cone whose vertex, H, is between the 
two bodies, and let this cone be indefinitely prolonged beyond Venus ; 
then will this prolongation embrace all the points from which any 
part of Venus will be projected on the face of the sun. As Venus 
moves past the earth, at the time of a transit, the advancing surface 



:.gx:::*m : ~ :---.:==:-r 

t). ** 

B 

Fig. 66. Solar Parallax by Delisle's Method 







of the cone will touch the surface of the earth (externally) at some 
point, A, at which the transit will begin earliest ; then, after sweep- 
ing over the earth, it will after a time become internally tangent at 
some point, B, at which the transit will begin latest. During the in- 
terval between these times of beginning, both planets being in motion, 
Venus will pass over a portion, VV, of its synodic orbit, the length of 
which in miles can be found from the length of AB, combined with 
the known positions and motions of the earth and Venus. 

In applying this method, two stations are selected, at one 
of which the phase to be observed begins early, and at the 
other late, and their latitudes and longitudes are carefully 
determined. The Greenwich time of the phase in question 
is noted at each station, and the corresponding interval is 
found. The length of the corresponding arc of the synodic 
orbit of Venus is then computed. From these data and the 
known synodic period of Venus the entire length of the 
orbit of Venus can be found, and consequently the distance 
of Venus from the sun can be determined in miles. From 
this we can readily deduce the solar distance of our earth 
and also the solar parallax. 

By observations on Mars when in opposition. 

The orbits of the earth and Mars are both excentric and 
their major axes are inclined to each other ; hence, the dis- 



148 ASTRONOMY. 

tances from the earth to Mars at different oppositions are 
widely different. The most favorable oppositions for de- 
termining the parallax are those that happen when Mars is 
nearest the earth, and these occur when Mars is- near its 
perihelion. Such an opposition occurred in 1877, and 
another will happen in 1892. 

When a favorable opposition takes place, two stations are 
selected as far apart as possible, one in the northern and 
the other in the southern hemisphere. From the former 
the planet is displaced towards the south, and from the 
latter towards the north. Observations are made at both 
stations for some time preceding and following the period 
of opposition, the displacements being determined by meas- 
uring the angular distance of Mars from certain fixed stars 
by means of a filar micrometer. The computations are 
made in the manner already explained for determining the 
lunar parallax, and from them we deduce the distance of 
Mars from the earth. This distance being known, the solar 
distance and parallax are readily determined. 

Observations may be made from a single station near the equator. 
Just after the rising of Mars lie is thrown toward the east by the 
effect of parallax, and just before setting lie is thrown toward the 
west. Between these times the observer is carried by the motion of 
the earth along an arc whose chord serves as a base line ; the principle 
is the same as before. 

By observations on the velocity of light. One of 
the most available, and perhaps one of the most reliable 
methods of determining the solar distance is by comparing 
the velocity of light with that of the earth, by means of the 
constant of aberration. The constant of aberration (Art. 
71), which is equal to 20".49, is the angle at the vertex of a 
right-angled triangle whose base is the velocity of the 
earth and whose altitude is the velocity of light ; hence, 
the velocity of the earth may be found when we know that 
of light, and from this the solar distance and parallax can 



THE SUN AND PLANETS. 149 

be deduced. One of the most recent and probably one of the 
most accurate determinations of the Telocity of light was 
made a short time since by Lieut. Michelson of the U. S. 
Navy ; he employed a modification of Foucault's appa- 
ratus, and obtained as a result the velocity 186,360 miles 
per second ; this velocity corresponds to a solar parallax of 
about 8". 8. 

Summary. The observations on the transits of Venus 
in 1761 and 1769 were carefully compared and discussed by 
Encke, who deduced for the solar parallax the value 
8". 587, a value that was used in computations for more 
than 30 years. This corresponds to a solar distance of more 
than 95,000,000 of miles. 

Since 1854 much doubt has existed as to the real value 
of the parallax, and many different opinions have been held 
by astronomers. All the recent observations, however, go 
to show that Encke's value is too^ small. 

Prof. Newcomb, in his Popular Astronomy, says : " It 
would appear that the solar parallax must lie between 
pretty narrow limits, probably between 8". 82 and 8".86, and 
that the distance of the sun in miles probably lies between 
92,200,000 and 92,700,000." Prof. Young, in his recent 
valuable work on the sun, says : " It would seem that the 
solar parallax cannot differ much from 8". 80, though it 
may be as much as 0".02 greater or smaller; this would 
correspond, as has already been said, to a distance of 
92,885,000 miles." 

A mere statement of the solar distance in miles conveys but a 
feeble idea to the mind of one who is not trained to contemplate 
the gigantic distances of astronomy. To compare it with familiar 
things, let us consider the rate of motion of an express train on one 
of our best railways. The speed of such a train hardly exceeds 38 
miles an hour, at which rate it would have to run day and night 
for 3 entire years to accomplish a single million of miles, or more 
than 277 years to pass over a distance equal to that which separates 



150 ASTRONOMY. 

us from the sun. And yet we shall find that the solar distance, enor- 
mous as it is, sinks into insignificance in comparison with that which 
intervenes between the sun and the nearest fixed star. 



Diameter, Surface, and Volume of the Sun. 

116. The diameter of the sun in miles is equal to the 
solar distance multiplied by the natural sine of its angular 
semi-diameter. Assuming the solar distance given by New- 
comb, this diameter is about 860,000 miles, or in round 
numbers it is about 109 times the equatorial diameter of 
the earth. 

The surfaces of spheres are to each other as the squares 
of their radii, and their volumes are to each other as the 
cubes of their radii. Hence, the surface of the sun is 
nearly 12,000 times as great as that of the earth, and his 
volume is about 1,280,000 times the volume of the earth. 

If we represent the earth bg a ball 1 inch in diameter, the sun, on 
the same scale, would be represented by a globe 9 feet in diameter, 
and the distance between the two globes would be more than £ of a 
mile. 

Mass of the Sun. 

117. We may find an approximate value for the mass of 
the sun in terms of that of the earth by comparing the 
sun's attraction on the earth with the earth's at- 
traction on the moon, in accordance with the laws of 
motion and gravitation. 

Let us suppose the orbits of the sun and the moon to be circles, the 
radius of the former being denoted by R, and that of the latter by r ; 
denote the mass of the sun by M and that of the earth by m ; also 
denote the sun's attraction on a unit of mass at the earth's distance by 
F, and the earth's attraction on a unit of mass at the moon's distance 
by/. Then, from the law of universal gravitation (Art. 52), we have 

M m 

F:/:: R r^ " •' " ' (1) ' 



THE SUN AXD PLANETS. 151 

Because action and reaction are equal (Mech., Art. 12), the attrac- 
tion of the sun on a unit of the earth's mass is equal to the centrifu- 
gal force of that unit, and this, by a law of mechanics, is equal to the 
square of its velocity divided by the radius of curvature of its path. 
If we now denote the earth's periodic time by T, the length of her 
orbit will be 27rR, and her velocity will be equal to 2rrR -r- T. Squar- 
ing this, dividing by R, and making the result equal to F, we have 

4rr2R 
F = ^pT (2). 

In like manner if we denote the moon's sidereal period by t, we 

have 

47r 2 r 

f=-r (3 >- 

Substituting these values of F and /in (1), and suppressing the com- 
mon factor, 4:r'-, we have 

R r M m 

T 2 : t? : : R* : r* ^' 

from which we find 

m~r*T> W- 

Making R = 92,500,000, r = 239,000, T = 365.256, and t = 27.32, which 

M 

are only approximate values, and reducing, we find — = 324,340, which 

differs by less than 1 % from that given in Table II., Art. 47, a value 
that was computed from more accurate data. 

Masses of the Planets. 

118. Formula (5) of the last article can be used for finding the 
mass of any planet having a satellite ; for we may make T equal to 
the planet's periodic time ; R, its distance from the sun ; t, the time of 
revolution of the satellite : and r, its distance from the planet. Then, 
because M is known, we can deduce the value of m, which in this case 
will be the mass of the planet. Mercury and Venus having no satel- 
lite, their masses must be determined from the perturbations produced 
by their attractions on other bodies of the system. The results of 
these computations are given in Table II., Art. 47. 

The Sun's Light and Heat. 

119. Many experiments have been made to determine 
the light given out by the sun in terms of what physicists 



152 ASTRONOMY. 

call a candle power, and though successful to a certain 
degree, the results expressed in figures are so enormous as 
to be almost unintelligible. 

More satisfactory results have been reached in comparing 
the relative brightness of different parts of the solar disk. 
These comparisons show that the disk is brightest at its 
centre, and that the brightness diminishes, at first slowly 
and then more and more rapidly as we approach its edge, 
where, according to Pickering, it is no more than |ths of 
what it is at the centre. 

It has been shown by experiment that the amount of 
heat received from different parts of the solar disk varies 
according to a similar law, though its diminution in ap- 
proaching the edge is not so rapid as in the case of light. 
Prof. Langley found that the heat received from a small 
area near the border of the disk was about J of that received 
from an equal area at its centre. 

These results seem to show that the sun is surrounded 
by an absorbing medium whose action on light and heat is 
similar to that of the terrestrial atmosphere. At the centre 
of the disk the rays of light and heat pass directly through 
the medium, and consequently experience a minimum 
amount of absorption. In approaching the border of the 
disk the rays pass through a continually increasing thick- 
ness of the medium, and consequently experience a contin- 
ually increasing amount of absorption. 

In 1838 Sir John Herschel undertook a series of observa- 
tions to determine the sun's annual expenditure of heat. 
By means of a suitable apparatus he allowed a beam of solar 
rays, 3 inches in diameter, to fall perpendicularly on a ves- 
sel containing a known quantity of water, and after a cer- 
tain time he observed the increase in the temperature of 
the water. From the data thus obtained he computed the 
amount of heat that falls upon a square yard perpendicu- 
larly exposed, and found that it was sufficient to melt a 
layer of ice having the same area and a thickness of 1 inch 



THE SUK AKD PLAtfETS. 153 

in about 2 hours and 13 minutes. Now, because the sun 
radiates heat equally in all directions, the entire amount of 
heat given out by the sun in 2 hours and 13 minutes is suf- 
ficient to melt a spherical shell of ice whose thickness is 1 
inch and whose radius is the distance from the sun to the 
earth. It has been shown that this enormous amount of 
heat is equal to that which would be produced by the com- 
bustion of a layer of anthracite coal extending over the en- 
tire surface of the sun and 35 feet in thickness. A simple 
computation will show that the heat given out by the sun 
in 6000 years would be more than that which would be pro- 
duced by the combustion of a volume of coal equal to that 
of the entire sun. 

The Sun's Probable Constitution. 

120. Recent researches lead to the belief that the sun 
consists of the following parts : 1°. A great central mass 
called the nucleus ; 2°. A shining, cloud-like envelope, 
8 or 10 thousand miles in thickness, surrounding the nu- 
cleus, and called the photosphere ; 3°. An envelope of 
gases and vapors, 3 or 4 thousand miles in thickness, lying 
immediately outside the photosphere, and called the chro- 
mosphere; and 4°. An extremely tenuous atmospheric 
envelope, lying outside the chromosphere, and of unknown 
extent, called the corona. 

In this description it is not to be supposed that these 
parts are separated by definite surfaces, or that the en- 
velopes themselves are of uniform thickness throughout; 
all that is intended is to convey an idea of the order in 
which the parts are situated with respect to each other. 

The Nucleus. 

121. The nucleus of the sun forms at least nine-tenths 
of its entire volume, but being hidden from view by the 
intervening photosphere, we know little or nothing of its 
actual constitution. Some astronomers suppose that it is 



154 ASTRONOMY. 

composed of substances similar to those that make up our 
earth, but so intensely heated that they cannot combine 
either chemically or physically, that is, they exist in a state 
that has been called dissociation. According to this view 
we may regard the solar nucleus as a mixture of metallic 
and other gases, so compressed that their average density is 
nearly 1J times that of water. Inasmuch as we have noth- 
ing of an analogous description on our earth, it is almost 
impossible to reason either on the properties of such a body 
or on the conflicting forces that must be in constant activity 
among its ultimate atoms. It is not unreasonable to sup- 
pose that it is subject to great internal disturbance, and 
this supposition is rendered more than probable by the 
gigantic commotions that are continually manifested, both 
in the photosphere and in the chromosphere. This suppo- 
sition with regard to the nature of the nucleus involves as a 
necessary consequence a continually increasing temperature 
as we approach its centre. 

Before proceeding to a study of what may be called the solar enve- 
lopes, it will be necessary to explain the construction and use of the 
spectroscope. 



The Spectroscope. 

122. A spectroscope is an instrument used in analyz- 
ing light. It consists essentially of three parts : 1°, a col- 
limator whose function it is to form a flat beam of parallel 
rays ; 2°, either a prism or a finely-ruled surface which 
disperses this beam so as to form a spectrum; and, 3°, 
a view-telescope, by means of which the different parts 
of the spectrum may be examined. 

In some of the best modern spectroscopes the spectra are 
formed by reflection from a ruled surface ; when, however, 
they are formed by refraction the requisite amount of dis- 
persion is obtained by using a train of prisms. 



THE SUN AND PLANETS. 



155 



The essential parts of a simple refracting spectroscope are 
shown in Fig. 67. The collimator, which resembles in 
appearance a small telescope, is shown at A. Instead of an 
eye-piece, there is a slit at K, through which the light to be 
analyzed is allowed to pass ; this slit is formed by means of 
two parallel jaws of metal which can be moved by screws 
so as to make the opening as narrow or as wide as desirable ; 
at L is a lens which can be so adjusted as to make the rays 
coming from the slit parallel to each other ; we then have a 
flat beam of light whose plane, like the direction of the slit, 
is perpendicular to the plane of the paper. The refracting 
prism is shown at B, its edges being perpendicular to the 
plane of the paper. The prism is made of dense glass 
with a refracting angle N, equal to about 60° ; it can be 
turned around an axis (not shown in the drawing) parallel 
to its refracting edge so as to make the angle of incidence 
equal to the angle of emergence, a position which is found 
to give the best results. The flat beam, in passing through 
the prism, is dispersed so as to form a spectrum, which can 
be seen by interposing a screen PO ; if the beam is com- 
posed of white light the red end of the spectrum will be at 
P and the violet end at 0. 




Fig. 67. The principle of the Spectroscope. 



Instead, however, of receiving the spectrum on a screen 
the deviated rays are allowed to fall upon the objective of 
the view-telescope, C, which differs in no material respect 
from an ordinary refracting telescope of low power. The 
telescope is attached to the frame of the instrument, and 



156 



ASTRONOMY. 



can be turned around an axis parallel to the edges of the 
prism ; if the dispersion is small the entire spectrum may 
be brought within the field of view, or if the observer de- 
sires it, the line of collimation may be made to coincide with 
any one of the refracted rays. 




Fig. 68. Perspective view of a simple Spectroscope. 

Explanation. B is the collimator ; P is the refracting prism : and A is the 
view-telescope. C is a tube which carries at the end nearest the light F a fine scale 
of equal parts photographed on glass ; the divisions of the scale, illuminated by the 
light F, are thrown on the face of the prism P, whence they are reflected into the tele- 
scope A ; the observer sees the divisions of the scale superposed on the spectrum 
formed by refraction, and is thus enabled to locate the lines observed in the spec- 
trum. 



If the telescope is pointed at P (Fig. 67), the observer sees a 
red image of the slit ; that is, a red line perpendicular to the 
plane of the paper ; if pointed at 0, he sees a violet image 
of the slit ; if pointed at any intermediate point, he sees an 
image of an intermediate color. In a word, the spectrum 



THE SUN AND PLANETS. 157 

is composed of a succession of images of the slit, each corres- 
ponding to rays of different degrees of refrangibility. If a 
ray of any particular degree of refrangibility is wanting in 
the bundle of deviated rays, the observer will see at the 
corresponding point of the spectrum a black line. 

The positions of the different images, and also of the 
black lines, are determined by micrometrical measurements ; 
these positions may be given in terms of the equal parts of 
an arbitrary scale, or more satisfactorily in terms of the cor- 
responding wave-lengths 
of light. 

The relations of the 
different parts of the 
spectroscope are more 
fully shown in Fig. 68, 
which represents the 
form used in the labora- 
tory. 

In more complex re- 
fracting spectroscopes 
the flat beam is trans- 
mitted through a suc- 
cession of prisms, each 
of which aids in its dis- 
persion. The manner 
of increasing the power 

Of a SpectrOSCOPe is Fig ' 69 ' Method of increasing the dispersion 
, . V C n of light. 

shown in rig. 69. 

Principles of Spectrum Analysis. 

123. The principles of spectrum analysis are embraced 
in the following summary: • 

1°. The spectrum of an incandescent solid, liquid, 
or gas under high pressure, is continuous. 

$\ The spectrum of an incandescent body in a 




158 ASTRONOMY. 

gaseous state and under low pressure is discontin- 
uous, being made up of bright lines ; the order and 
the number of bright lines is characteristic, that is, 
it is always the same for the same substance. 

3°. *A- substance in a gaseous state absorbs from 
white light, when transmitted through it, the rays 
of which its own spectrum consists. 

As an illustration of the foregoing principles, let us con- 
sider the action of the vapor of sodium on the calcium 
light. If a piece of lime is rendered incandescent by heat- 
ing it in the oxy-hydrogen flame, its light, when transmitted 
through the spectroscope, gives a perfectly continuous spec- 
trum. Again, if sodium is made incandescent by burning 
one of its salts in a Bunsen burner, its light, when trans- 
mitted through the spectroscope, gives the bright-lined 
spectrum characteristic of sodium, the principal feature of 
which is a double line in the orange part of the spectrum. 
If now the light of incandescent lime is superposed upon 
that of the sodium by transmitting the former through the 
latter, there will result a continuous spectrum interrupted 
by a double black line occupying the exact place of the 
principal sodium lines ; the vapor of the sodium has ab- 
sorbed the corresponding rays of the calcium light. 

Chemical Constituents of the Sun. 

124. The solar spectrum when formed by a highly dis- 
persive spectroscope is found to be crossed by hundreds, 
even thousands, of dark lines and bands. Many of these 
have been found, by the principles explained in the last 
article, to correspond with the bright lines of the spectra 
of terrestrial substances, indicating that the solar light on 
its way to us has passed through and been acted upon by 
the vapors of those substances. Thus, of the 600 bright 
lines which constitute the complex spectrum of the vapor 
of iron, more than 450 have been recognized as correspond- 



THE SUN AND PLANETS. 159 

ing with the dark or reversed lines of the solar spectrum. 
More than one-third of the elements that we are acquainted 
with on our earth are known to exist in the sun. A few of 
the more common ones are iron, sodium, calcium, hydro- 
gen, manganese, nickel, cobalt, barium, strontium, lead, 
and titanium. 

Telescopic Appearance of the Photosphere. 

125. The photosphere, as its name implies, is the 
light-giving part of the sun. It surrounds the nucleus, and 
appears to be made up of enormous cloud-like masses, sus- 
pended as it were, in a medium which is nearly or quite 
transparent. These shining masses, for want of a better 
name, may be called clouds ; they differ, however, very 
materially from terrestrial clouds, inasmuch as the latter 
consist of watery vapor, whereas the former are made up of 
metals and other substances maintained in a vaporous con- 
dition by intense heat. It is thought by some that the 
photospheric cloud-forms are columnar in shape, and that 
the intervals between them are filled with matter 'thrown 
up from the interior regions of the sun. 

When viewed with a telescope of sufficient power the sur- 
face of the photosphere presents a mottled appearance, 
which Newcomb compares to that of a fluid in which 
ill-defined rice-grains are suspended ; Herschel says that 
nothing represents this appearance so faithfully as " the 
slow subsidence of some flocculent chemical precipitate 
in a transparent fluid when viewed perpendicularly from 
above;" Nasmyth likens the shape of the shining masses 
to willow leaves. It is not unlikely that the different ap- 
pearances described by observers are somewhat dependent 
on accidental circumstances, such as variations in the 
power of the telescope or in the clearness of the atmos- 
phere, and the like. 

The cloud masses that give to the photosphere its general 
mottled appearance are subject to considerable changes, 



160 ASTRONOMY. 

both in form and in magnitude, in consequence of which 
the actual appearance of the sun is not always the same at 
all points of its surface. These changes in the apparent 
character of the photosphere are particularly noticeable in 
the neighborhood of those dark patches yet to be described, 
and which are known as solar spots. 

The mottled character of the sun's surface is shown in 
Fig. 70, which also illustrates some of the curious appear- 
ances presented by the sun-spots yet to be described. 




Fig. 70. Sun Spot. Drawn by Prof. Langley. 

Explanation. This figure shows the mottled character of the sun's surface, 
and also shows a curious group of sun-spots. The circle in the upper left-hand 
corner represents our earth on the same scale. 

Faculae. 

126. Besides the shining cloud-tops that produce the or- 
dinary mottling, larger and brighter spots, called faculae, 
are frequently seen on different parts of the sun's surface. 
Sometimes they take the form of irregular luminous spots, 
and sometimes they are long and narrow, appearing like 
immense masses of photospheric matter heaped up in bil- 
lowy ridges. The faculae, which are particularly numerous 
in the neighborhood of solar spots, are seen to best advan- 
tage when they are near the border of the solar disk, an 



THE SUN AND PLANETS. 161 

effect which is probably due to perspective, in the same way 
that we have a more striking view of a mountain range 
when we look at it horizontally than when we look down 
upon it from above. 

The general appearance of the faculae is shown in Fig. 71, 
which is from a photographic view of a portion of the sun 
near its border. 



- . .. ... ■■— ■ • 




Fig. 71. Photographic view of Spots and Faculae. 

Explanation. Fig. 71 shows a line of solar spots with their surrounding 
faculae. The spot on the right-hand is foreshortened by perspective, and the faculae 
in its neighborhood are very conspicuous. 



Sun Spots. 

127. The dark patches on the solar disk, to which refer- 
ence was made in a preceding article, are called sun-spots ; 
they vary so much in many respects that a general descrip- 
tion of them is almost impossible. Sometimes they are 
nearly circular, but as a rule their outlines are exceedingly 
irregular ; sometimes they occur singly, but more frequently 
they are grouped in clusters like islands in the ocean ; some- 
times they are seen in vast numbers, and then again not a 
spot is to be seen ; an occasional spot may last for many 



162 



ASTEOKOMY. 



weeks, but such persistency is exceptional ; as a rule, the 
spots only continue for a few days, and not infrequently 
they close up and disappear in the course of a few hours; 
some are so small that they are only visible under high 
magnifying powers, some are many thousands of miles in 
extent, and occasionally one occurs that is large enough to 
be visible to the naked eye. 




Fig. 72 Sun Spots. Drawn by Trouvelot. 



A fully developed sun-spot, like the right-hand one in 
Fig. 72, consists of a dark central portion called the nu- 
cleus, surrounded by a lighter border called the penum- 
bra. The nucleus is separated from the penumbra, and the 
penumbra from the photosphere, by irregular but well de- 
fined lines. Under a high magnifying power the penumbra 
is seen to be striated, the filamentary masses which consti- 
tute the striae being directed towards the nucleus. Very 
often these filaments, which appear to consist of photo- 
spheric matter, extend far into the nucleus, and not infre- 
quently they reach entirely across, forming as it were lumi- 
nous bridges. It is a fact worthy of note, that the penumbra 
is brightest near the nucleus, growing darker as it ap- 
proaches the outer edge of the spot. 

The entire spot appears to be a cavity or rent in the 



THE SUN AND PLANETS. 



163 



photosphere, the central part, corresponding to the nucleus, 
being filled with comparatively non-luminous gases; the 
penumbra seems to be made up of columnar masses that 
have been detached from the photosphere and drawn in- 
ward amongst the gases that form the nucleus. According 
to this view, the crowding together of the photospheric 
filaments as they are drawn inward would account for the 
greater brightness of the penumbra in the neighborhood of 
the nucleus. Sometimes the filaments appear to melt away 
as they reach the nucleus, and at other times they assume 
curiously distorted forms as though they were acted upon 
by powerful conflicting forces. (See Fig. 70.) 



Illi ;,: S|;illiilSliil^ 




Fig. 73. Sun Spot. Drawn by Nasmyth. 

Fig. 73 represents a sun-spot drawn by Nasmyth. It shows the mottling pro- 
duced by the intersections of forms shaped like willow leaves. It also shows the 
manner in which spots are often cut up and divided by bridges and prolongations 
of the penumbral filaments. 



That solar spots are depressions in the photosphere is 
shown by their appearances when near the sun's limb ; when 
near the eastern border of the disk we see only the eastern 
portion, and when near the western border we see only the 



164 ASTRONOMY. 

western portion of the penumbra; in each case the opposite 
portions of the penumbra are apparently hidden by the in- 
tervening and more elevated part of the photosphere. In 
some cases a notch in the disk has been observed at the 
point where a spot is passing from the visible to the invisi- 
ble hemisphere of the sun. 

Rotation of the Sun. 

128. Solar spots, when observed from day to day, are 
found to move across the sun's disk in such a manner as to 
indicate that the sun revolves on an axis, turning from west 
to east and performing a complete revolution in about 25 
days. This axis prolonged northward meets the celestial 
sphere in the constellation Draco at a point which is about 
7° from the pole of the ecliptic and about 26° from the pole 
of the heavens ; that is, the inclination of the sun's equator 
to the ecliptic is about 7° and its inclination to the equinoc- 
tial is about 26°. 

The earth passes through the plane of the solar equator 
twice a year, once in the early part of June and again in 
the early part of December ; at these times the paths of 
the solar spots, which are circles parallel to the sun's equa- 
tor, are seen edgewise, and consequently appear to be 
straight lines ; at all other times they are seen obliquely 
and consequently appear to be elliptical. The curvilinear 
character of their apparent paths is most noticeable in the 
months of September and March. 

Eecent observations show that the different parts of the 
sun's surface do not all revolve in the same time, the angu- 
lar velocity being greatest near the equator and diminishing 
toward the poles. At the equator the time of revolution, 
as already stated, is about 25 days, and at a point 45° dis- 
tant from the equator the time is more than 27 days. The 
cause of this continued lagging motion as we recede from 
the solar equator has not been satisfactorily explained. 



THE SUN AND PLANETS. 



165 



Distribution and Periodicity of Spots. 

129. Spots do not occur with equal frequency at all 
points of the sun's surface, but are generally found within 
the limits of two zones, oue north and the other "south of 
the equator and extending from 8° to 40° of solar latitude ; 
they are most numerous in both zones between the parallels 
of 10° and 25° of solar latitude. In the immediate neigh- 
borhood of the equator they are seen but rarely, and the 
appearance of a spot beyond the parallel of 45° is excep- 
tional. 




Fig. 74. The Spotted Zones. 



Explanation. The outer circle represents the sun's disk. The solar equator 
i* parallel to the lower line of spots. 



166 ASTRONOMY. 

The tendency of spots to occur in zones or belts is shown 
in Fig. 73, taken from a drawing by Trouvelot. 

Furthermore, spots are not equally numerous in different 
years, their occurrence being subject to a pretty definite law 
of periodicity. The attention of astronomers was called to 
this law by Schwabe of Dessau, who published in 1851 the 
results of 25 years observation on solar spots. He con- 
cluded as the result of his labors that the spots increase 
and diminish periodically, both in respect to frequency and 
size. He assigned a period of about 10 years as the length 
of the cycle of change. 

The conclusions of Schwabe with respect to the periodicity 
of sun-spots has been confirmed by subsequent investigations, 
particularly by those of Wolfe, who made an exhaustive 
examination of the subject. Wolfe assigns as the average 
length of a spot cycle 11.1 years; that is, about 9 cycles in 
a century. It is now conceded that the cycles are of varia- 
ble length, sometimes being only 8 or 9 years, and some- 
times amounting to 15 or 16 years. It is a curious fact 
that the fluctuations of terrestrial magnetism are also 
periodic, the cycles corresponding closely with the sun-spot 
cycles. The periods of greatest magnetic disturbance appear 
to correspond with the maximum of sun-spots, and those 
of least magnetic disturbance with the minimum of sun- 
spots. The auroral phenomena also seem to conform to a 
similar law of periodicity. 

The Chromosphere. 

130. Immediately above the photosphere, and resting 
upon it, is an envelope three or four thousand miles in 
thickness, which, on account of its brilliant scarlet color, 
has been named the chromosphere. It consists of a mix- 
ture of incandescent gases and vapors, the most marked 
constituent and the one to which its color is due being 
hydrogen. Prof. Young says that it appears "as if count- 
less jets of heated gas were issuing through vents and spira- 



THE StJtf AXD PLAXETS. 16? 

cles over the whole surface, thus clothing it with flame 
which heaves and tosses like the blaze of a conflagra- 
tion." 

The dense vapors of iron, barium, sodium, manganese, 
magnesium, nickel, titanium, calcium, strontium, and the 
like, are found at the bottom of the envelope, whilst the 
upper regions in their normal condition consist almost en- 
tirely of hydrogen. The denser vapors are, as a rule, found 
in a stratum which is not more than five or six hundred 
miles in thickness, the remaining part consisting of in- 
candescent hydrogen. For this reason, some solar physicists 
have been inclined, perhaps without sufficient reason, to re- 
gard what we have called the chromosphere as two separate 
envelopes, calling the lower one the reversing layer, and 
the upper one the chromosphere. 

The lower surface of the chromosphere conforms to the 
upper surface of the photosphere, but its upper surface is 
very rough and irregular, presenting an appearance that 
may be likened to a gigantic ocean of billowy flame. At 
the time of a total solar eclipse the chromosphere, and par- 
ticularly its upper regions, may be seen with an ordinary 
telescope ; but by the aid of the spectroscope it may be seen 
and studied at other times. 

The reversing layer, when viewed along the sun's border 
by means of the spectroscope, gives a bright-line spectrum, 
corresponding to the materials of which it is composed ; but 
the white light from the photosphere shining through it is, 
in accordance with principle 3°, Art. 123, partially absorbed, 
and the corresponding spectrum is, interrupted by black 
lines ; hence, the name reversing layer. The upper layer 
seems to be the principal origin of the solar protuber- 
ances described in the next article, though it is believed 
that the occasional evidences of other matter than hydro- 
gen are due to matter thrown up from the lower or re- 
versing layer. 



168 ASTKOHOMY. 



Solar Protuberances. 



131. Observation shows that the chromosphere is a re- 
gion of intense commotion; under the action of enormous 
forces it is kept in a state of continual agitation, and fre- 
quently huge masses of chromospheric matter are projected 
into the overlying solar atmosphere, constituting what are 
called solar protuberances. These brilliant, cloud-like 
prominences, which consist principally of incandescent hy- 
drogen, though sometimes containing other substances, are 
undoubtedly scattered over the entire surface of the sun, 
but owing to the dazzling brightness of the photosphere we 
can see only those which are situated near the border of the 
solar disk. Some of these rise to great heights, and are 
often seen during the time of a total solar eclipse projecting 
from behind the black disk of the moon like vast tongues 
of flame. 

Prior to 1868 no protuberances had been seen except at 
the time of a solar eclipse, but in that year it was discov- 
ered, almost simultaneously by Lockyer and Jansen, that 
they may be seen and studied at any time when the sun is 
visible. 

The instrument employed for this purpose consists of a 
spectroscope attached to an equatorial telescope, the combi- 
nation constituting what is sometimes called a telespectro- 
scope. In order to see a protuberance the telescope is 
directed so that the slit of the spectroscope shall be tan- 
gential to the sun's disk, and then the slit is slightly 
opened. The light that comes from the protuberance is 
not dispersed, whilst that from the surrounding region is 
so much scattered as to render the protuberance visible. 

Solar protuberances differ widely in magnitude and in 
general appearance. Of 2,767 measured protuberances re- 
ferred to by Young in his book on the sun, fully two-thirds 
of the whole were more than 18,000 miles in height, nearly 
one-quarter of the whole were over 28,000 miles high, and 



THE SUK AKD PLANETS. 169 

several reached an altitude of more than 84,000 miles. He 
says that he has seen three or four whose heights were more 
than 150,000 miles, and that Secchi saw one whose altitude 
was over 300,000 miles. He also says that he himself ob- 
served one which attained the unprecedented height of 
350,000 miles. When first seen this protuberance had an 
altitude of only 40,000 miles, and therefore attracted no 
special attention. He then goes on to say : " When next 
seen, half an hour later, it had become very brilliant, and 
had doubled its height ; during the next hour it stretched 
upward until it reached the enormous altitude mentioned, 
breaking up into filaments which gradually faded away, 
until by 12.30 p.m. there was nothing left. A telescopic 
examination of the sun's disk showed nothing to account 
for such an extraordinary outburst, except some small and 
not very brilliant faculae." 

The protuberances vary as much in appearance as they 
do in magnitude. Some resemble masses of clouds stretch- 
ing along the solar disk like sierras, or perhaps floating in 
the solar atmosphere, either entirely detached from the 
disk, or connected with it by slender filaments. Others 
take the form of jets as if shot forth from the sun with 
enormous energy, sometimes combing over and descending 
like ocean breakers, and at other times apparently rent asun- 
der and shattered by contending forces, as shown in Fig. 75. 




Fig. 75. Solar Protuberances. Drawn by Trouvelot. 

Sometimes the protuberances assume arborescent forms, as 
shown in Fig. 76. 
8 



170 ASTROKOMY. 




Fig. 76. 

In all cases their shapes are indicative of gigantic forces, 
sometimes acting, normally from below, and sometimes 
sweeping along the surface of the sun, either progressively, 
or in a revolving direction like a vast cyclone. 

The Corona. 

132. The corona, which has never been seen except 
during a total solar eclipse, is an envelope of complex con- 
stitution, lying above the chromosphere, and extending out- 
ward to a distance that has not yet been determined. At 
the time of totality it is seen surrounding the dark body of 
the moon as a riug of silvery light, often crossed by radiating 
streaks, which give it an appearance that has been likened 
to the halo of glory that we sometimes see depicted around 
the heads of saints. The part next the sun, and extending 
outward to the distance of a tenth of its radius, is very 
bright and tolerably uniform in appearance; the radiating 
streaks or beams, which are frequently inclined and curi- 
ously bent, are irregularly distributed around the sun ; in 
some places they are few in number and comparatively 
short, and again in other places they are very numerous, 
and extend outward to enormous distances, so that the visi- 
ble outline of the corona is usually jagged and extremely 
irregular. 

The jagged outline of the corona is shown in Fig. 77, 
which represents its appearance as drawn by Foenander 
during the total eclipse of 1871. 



THE SUN AND PLANETS. 



171 




Fig. 77. Corona seen in 1871. 



The general appearance of the corona is never the same 
at two different eclipses, and even at the same eclipse 
observers differ in their account of its outline, especially if 
their observations are made at different stations. Some- 
times the radial wings are seen to extend to great distances 
in the direction of the solar equator. An example of this 
kind is shown in Fig. 78, which represents the corona as 
seen by Bullock during the eclipse of 1868. 

Prof. Young, in speaking of the corona, says " that of the 
eclipse of 1878 is remarkable on account of the enormous 
extension of the faint brushes of nebulosity, which were 
traced to a distance of 6° or 7° from the sun by Professors 
Langley, Abbe, and Newcomb." It is to be noted that an 



172 ASTROHOMY. 

angle of 6° at the sun's distance corresponds to a distance 
of more than 9,000,000 of miles. 




Fig. 78. Coi-ona as seen in 



The peculiar form of the corona as seen during the 
eclipse of 1878 by a party of astronomers in Texas is 
shown in Fig. 79. 




Fig. 79. Corona as seen in 1878 in Texas. 



THE STO AND PLANETS. 173 

But little is known about the physical constitution of the 
corona; it has even been suggested that it is an optical 
phenomenon, and some weight has been given to this sug- 
gestion by the observations recently made at the Caroline 
Islands on the eclipse of May 6, 1883. Previous observa- 
tions, however, leave but little room to doubt that it con- 
sists, in part at least, of gases far more tenuous than any 
with which we are acquainted on our earth. The corona 
was carefully observed with the spectroscope during the 
eclipse of 1869 by Professors Young and Harkness ; they 
found in its spectrum a greenish bright line, corresponding 
to the number 1-474 of KirchofFs scale. Subsequent obser- 
vations have shown numerous dark lines, corresponding to 
the dark lines of the solar spectrum. These observations 
would seem to indicate that the corona contains a glowing 
gas in which is suspended a certain amount of matter which 
is capable of reflecting solar rays. 

The Zodiacal Light. 

133. The zodiacal light is a lenticular-shaped blush 
of light that is visible in the western sky after sunset in 
early spring, and in the eastern sky before sunrise in early 
autumn. 

Its base, which is 10° or 15° in breadth, rests on the hori- 
zon, its axis coincides sensibly with the ecliptic, and its 
apex is 30° or 40° from its base. It is generally less lumi- 
nous than the milky way, and its edges are not so well de- 
fined ; for these reasons it is very difficult to determine its 
exact limits. 

It is seen to best advantage in the evenings about the 
time of the vernal equinox, and in the mornings about the 
time of the autumnal equinox, because at those times its 
axis makes the greatest possible angle with the horizon. 

Within the tropics it is a conspicuous object, and is visi- 
ble at all seasons, both in the evening and in the mornings 



174 ASTKONOMY. 

Under favorable conditions the light is visible both in the 
east and in the west at midnight ; it has even been seen 
extending across the entire heavens from horizon to horizon. 

Humboldt, speaking of its brilliancy in the tropical re- 
gions, says: " Those who have lived for many years in the 
zone of palms must retain a pleasing impression of the mild 
radiance with which the zodiacal light, shooting pyramid- 
ally upwards, illuminates a part of the uniform lengths of 
tropical nights. I have seen it shine with an intensity 
equal to that of the Milky Way in Sagittarius." 

The intensity of the zodiacal light is somewhat variable, 
but whether its variations are periodic or not is unknown. 
The fact of its variability is testified to by Humboldt, who 
had ample opportunity for observation during his long stay in 
South America. It is also noticed, even in our unfavorable 
situation for observation, that the intensity of its light varies 
from night to night and from season to season more than 
would seem to be due to varying atmospheric conditions. 

Various theories have been proposed to account for this 
phenomenon, the most plausible one being that it is due 
to a ring of meteorites revolving around the sun, each 
meteorite being too small to be separately visible, but 
aggregated in such numbers as to reflect a considerable 
amount of solar light. 



VII. ECLIPSES. 



Definitions. 



134. A solar eclipse is an obscuration of the sun caused 
by the passage of the moon between it and the observer. 

A lunar eclipse is an obscuration of the moon caused 
by her entrance into the earth's shadow. 

A solar eclipse can occur ouly at the time of new moon, 
and a lunar one only at the time of full moon ; and even at 
those times no eclipse can take place unless the moon hap- 
pens to be very near the plane of the ecliptic. 

Shadow Systems of the Earth and Moon. 

135. In Fig. 80, let S represent the sun, E the earth, 
and suppose two cones of rays to be drawn tangent to both 



Fig. 80. Section of Shadow System by a Plane through its Axis. 

bodies, the vertex of the first being beyond the earth, and that 
of the second being between the earth and the sun. The 
part of the first cone, which lies between E and the vertex 
V, is the umbra, or shadow proper of the earth ; the pro- 
longation of this cone beyond V is called the second 
nappe of the shadow cone ; and that part of the second 
cone lying beyond E and outside of the first cone, is called 
the penumbra, or partial shadow ; all these taken together 
Constitute the earth's shadow system. The moon in like 



176 ASTEOKOMY. 

manner has a similar shadow system, consisting of umbra, 
second nappe ,and penumbra. 

The length of the earth's umbra can easily be found in terms of 
the solar distance : 

Let S and E represent sec- 

^ tions of the sun and earth 

s' 7^s~~- — ->^_^ r Dv a plane through their cen- 

f Cy V— — -—^^>y^ — _^^^ treg> gy their line of centres, 

I $ J 5 \jt~) l V an( ^ ^ an externa l tangent. 

V^ ^/ Draw SA and EC perpendicu- 

Fig. 81. Diagram. lar to AV, and CD parallel to 

VS. Denote SA, the radius 

of the sun, by R; EC, the radius of the earth, by r ; SE, the earth's 

distance from the sun, or its equal DC, by D ; and EV, the length of 

the umbra, by I. From the similar triangles DAC and ECV, we have 

DA : DC : : EC : EV, or R -r : D : : r : I, 

■}.:>*& » 

If we assume that the sun's radius is 109 times that of the earth, 

which is verv nearly true, we have R — r = 108r, whence I = — — ■ that 

is, the length of the earth's umbra is equal to the earth's distance from 
the sun divided by 108. 

In like manner, by assuming the sun's radius to be 400 times that 
of the moon, which is sufficiently accurate for our purpose, we find 
that the length of the moon's umbra is equal to the moon's distance from 
the sun divided by 399. 

When we know the length of the shadow, and the diameter of the 
body which casts it, we can find the diameter of the cross-section of 
the shadow at any distance, x, from its apex. For if we denote the 
diameter of«the body by d, the diameter of the shadow's cross-section 
by d' , the length of the shadow by I, and the distance of the section 
from the apex by x, we shall have 

d : d< :: I : ; x } .-. d! = ~ (2). 

Formula (2) is equally applicable when x is measured on the pro- 
longation of I, that is, when the section is made in the second nappe. 

If we change — r into +r, formula (1) will be applicable to finding 
the vertex of the penumbral cone of either the earth or the moon. 



ECLIPSES. 177 

Thus, the vertex of the moon' s penumbral cone lies between the sun and 
moon, and at a distance from the latter equal to her distance from the 
sun divided by 401. 



Kinds of Solar Eclipses. 

136. Whenever any part of the moon's shadow system 
sweeps over the earth there is a solar eclipse which is visible 
from every point on which the shadow falls. To an observer 
within the penumbra, the eclipse is partial, and the visible 
part of the sun's disk is crescent-shaped ; to an observer 
within the umbra, the eclipse is total, no part of the sun's 
disk being visible ; to an observer in the second nappe of 
the umbra, the eclipse is annular, that is, a portion of the 
sun's disk is seen completely surrounding the moon like a 
ring. To an observer in the axis of the shadow system, 
the eclipse is central, and may he either total or annular ; 
in the latter case the visible ring of the solar disk is of uni- 
form width throughout. 

An eclipse when considered with respect to a given point 
is said to be local ; when considered with respect to the 
whole earth, it is general. 



Solar Ecliptic Limits. 

137. In order that a solar eclipse may be possible at the 
time of any new moon, it is necessary that the moon should 
be near enough to the plane of the ecliptic to bring some 
part of her disk between the observer and the sun. This 
can only happen when the sun is near the moon's node at 
the time of conjunction. 

It has been found by computation that a solar eclipse 
is impossible when the sun, at the time of new moon, is 
more than 18°. 5 from the moon's node, and that an eclipse 
is certain when this distance is less than 15°. These dis- 
tances are called the solar ecliptic limits. If at the 



178 ASTRONOMY. 

time of conjunction the sun's distance from the node lies 
between these limits, the occurrence or non-occurrence of 
an eclipse must be determined by calculation. 

In order that a solar eclipse may be central, the line pass- 
ing through the centres of the sun and moon must strike 
the earth. This cannot happen if the sun at the time of 
new moon is more than 11°.9 from the lunar node, and it is 
certain to happen if this distance is less than 9°.5. If the 
sun's distance from the node, at the time of conjunction, lies 
between these limits, the occurrence or non-occurrence of a 
central eclipse must be determined by computation. 

Of the Central Eclipse. 

138. The central eclipse will be total whenever the 
moon's umbra is long enough to reach the earth ; in all 
other cases it will be annular. 

The length of the moon's umbra, in any given case, is 
easily found ; for, we have only to divide the moon's dis- 
tance from the sun by 399 (Art. 135). Knowing this 
length and the moon's distance from the earth, we can at 
once decide whether the eclipse will be total or annular. 

Let it be required to find the greatest and the least lengths of 
the moon's umbra at the time of conjunction. For this purpose let 
us assume that the greatest distance from the sun to the earth is 
94,000,000 miles, and that his least distance is 91,000,000 miles ; also 
that the greatest and the least distances of the moon from the earth 
are 252,000 miles and 226,000 miles. 

Now it is obvious that the moon's umbra will be longest at the time 
of conjunction when the sun is farthest from, and the moon is nearest 
to, the earth. In this case the moon's distance from the sun is 
93,774,000 miles, and by the rule above given, the corresponding 
length of the umbra is 235,000 miles. Hence, the umbra extends 
9,000 miles beyond the earth's centre, or about 13,000 miles beyond 
the nearest point of the earth's surface. (Fig. 82.) 

The moon's umbra will be shortest at the time of conjunction when 
the sun is nearest to, and the moon farthest from, the earth. In this 
case the moon's distance from the sun is 90,748,000 miles and the cor- 



ECLIPSES. 179 

responding length of the umbra is about 227,400 miles. Hence, the 

umbra falls short of the earth's centre by 24,600 miles, and of the 

nearest point on the earth's surface by about 20,000 miles. (Fig. 83.) 



Limits of Visibility. 

139. From what was stated in Art. 136, it is plain that a 
partial eclipse will be visible from every part of the earth's 
surface which is swept over by the moon's penumbra, that 
a total eclipse will be visible from every part of the belt 
or zone swept over by the umbra, and that an annular 
eclipse will be visible from every part swept over by the 
second nappe of the nmbra. 

Let us first consider the case in which the moon's umbra is longest, 
its axis being perpendicular to the earth's surface, as shown in Fig. 82. 

Explanation. M is the moon, y -•>. 

Eis the earth, and MV the moon's P'l^jnmni^ \ 

umbra when its axis is perpen- ( ^'' i '.f' jjjjijj j [jfjflA E* X =-\7 

dicular to the earth's surface, the Vjj§§|U "J" 

umbra being at its longest. The ~x^ ^y 

space between the umbra and the 

broken lines in the figure is the Fig. 82. Maximum Visibility of Total Eclipse. 



penumbra. 

The distance AV being 13,000 miles, we can easily compute the 
cross-section of the umbra at A, by means of the principles explained 
in Art. 135 ; in the case under consideration this cross-section is found 
to be a little less than 120 miles. This would be the greatest breadth 
of the moon's shadow, and consequently of the zone of totality, if the 
axis of the shadow were always perpendicular to the earth's surface, 
but as the shadow sweeps over the earth its axis falls more or less 
obliquely upon the earth ; hence, it may happen that the breadth of 
the shadow will be considerably greater than 120 miles. If the sun 
is nearer the earth than we have supposed, or if the moon is more 
distant, the breadth of the zone of totality will be correspondingly 
narrower ; it may even reduce to a mere line. 

In the case considered the breadth of the penumbra, BC, is more 
than 4,200 miles ; this indicates the breadth of space from which the 
eclipse is partially visible, 



180 



ASTKONOMY. 



Let us next consider the case in which the moon's umbra 
is shortest, its axis being perpendicular to the earth's sur- 
face as shown in Fis'. 83. 




Fig. 83. 



Maximum Visibility of Annular, 
Eclipse. 



Explanation. In this figure the 
explanation is the same as before, 
except that VA is a part of the um- 
bra's second nappe. 



The distance VA being 20,600 
miles, we find the diameter of 
the cross-section of the second 
nappe at A to be something greater than 190 miles, and the diameter 
of the penumbral section at BC to be more than 4,500 miles. 

In consequence of the obliquity of the shadow-cone's axis to the 
surface of the earth, we see that the breadth of the zone from which 
an annular eclipse is visible may be something greater than 190 miles. 
In a majority of cases it is much narrower; it may even be reduced to 
a mere line. 



The Moon's Relative Orbit. 

140. In discussing the circumstances of an eclipse, 
whether local or general, it is found convenient to suppose 
the sun to remain at rest and the moon to move with 
the relative motion of the two bodies. The path' that the 
moon appears to follow is then called the moon's relative 
orbit. 




To explain what is meant by 
the moon's relative orbit, let SN 
(Fig. 84) be the ecliptic and MN 
the moon's actual orbit, both pro- 
jected on a plane perpendicular to 
the line of nodes of the moon's 
orbit. Let S and M be the places 
of the sun and moon at the time 

of conjunction in longitude. Draw MA parallel to SN, and make it 
equal to the moon's hourly motion in longitude diminished by the 
sun's hourly motion in longitude j draw AC perpendicular to MA and 



N S 

Fig. 84. The Moon'6 Relative Orbit. 



ECLIPSES. 181 

make it equal to the moon's hourly motion in latitude, then will a 
line through M and C be the moon's relative orbit, and the distance 
from M to C will be the moon's hourly motion with respect to the sun. 
If we draw SO perpendicular to MC, the point O will be the relative 
place of the moon at the time of nearest approach of the centres of the 
sun and moon, and MO expressed in terms of MC will represent the 
fractional part of an hour that constitutes the interval between the 
time of conjunction and the time of nearest approach, which last is 
obviously the same as the time of the middle of the eclipse. 

Of the Local Solar Eclipse. 

141. The circumstances of a local eclipse that are usually 
predicted by astronomers, and laid down in the almanacs are 
the times of beginning, middle, and ending ; also in case of 
a total eclipse, the times of beginning and ending of totality ; 
and in case of an annular eclipse the times of formation and 
rupture of the ring. 

In the case of a partial eclipse the magnitude is gener- 
ally given, that is, the fractional part of the sun's disk that 
is covered at the time of greatest obscuration. 

The time of beginning is the instant at which the eastern 
limb of the moon appears to touch the western limb of the 
sun. From this time the form of the sun's visible disk may 
be described as crescent, the line joining its horns or cusps 
being always perpendicular to the line of centres of the solar 
and the lunar disks. 

The middle of the eclipse is the instant the centres of the 
two disks are nearest to each other. At this time the line 
of cusps is parallel to the moon's relative orbit. 

The time of ending is the instant at which the western 
limb of the moon appears to separate from the eastern limb 
of the sun. 

The times of these different phases of a solar eclipse depend not 
only upon the relative motion of the moon with respect to the sun, 
but also upon the actual motion of the observer in consequence of 
the earth's axial rotation. 



182 ASTKONOMY. 

The magnitude of the eclipse is measured by the greatest 
breadth of the obscured portion of the sun's disk. This is 
expressed in terms of the sun's diameter, sometimes deci- 
mally, and sometimes in digits, a digit being the twelfth 
part of a diameter. Thus, if three-fourths of that diameter 
of the sun which is directed toward the moon's centre is 
covered by the moon's disk, the eclipse is said to have a 
magnitude of .75, or of 9 digits. 

For the method of computing the times of the above phenomena 
the student is referred to Looniis' Practical Astronomy. 

Of the General Solar Eclipse. 

142. In considering the general eclipse it is to be borne 
in mind that the moon's shadow system is sweeping east- 
ward across the earth by virtue of the moon's motion along 
her relative orbit, and also that every place on the earth is 
at the same time moving from west to east, but less rapidly, 
by reason of the earth's rotation on her axis. The circum- 
stances resulting from a combination of these motions are 
predicted by astronomers, and graphically recorded by 
means of maps like that shown in Fig. 85, which was con- 
structed to illustrate the annular eclipse of October 19, 
1865. The figure and its explanation, copied from an alma- 
nac of that year, show the usual method of recording cer- 
tain specific details of a general eclipse. 

In order to explain the lines laid down on the map, let us suppose a 
plane to be passed through the centres of the sun and moon and per- 
pendicular to the plane of the moon's orbit.' This plane, which may be 
called the central plane, is supposed to follow the moon in its motion, 
always dividing its umbra and penumbra into two symmetrical parts, 
an eastern or preceding part, and a western or following part. It is 
obvious that the eclipse is just beginning to an observer who is any- 
where on the surface of the preceding part, and just ending to an ob- 
server who is anywhere on the surface of the follomng part 

When the preceding surface of the moon's penumbra strikes the 
earth the general eclipse begins, and the point at which the contact 



ECLIPSES. 



183 



takes place is marked first contact on the map. Because the element 
of the penumbral cone that determines the place of contact is a solar 
ray tangent to the earth's surface, the sun must be in the eastern hori 




Fig. 85. General Eclipse of October, 1865. 

Explanation. The eclipse first touches the earth in long. 30° 51' 12" W. of 
Washington, in lat. 35° 7 30" N., at the instant of sunrise there, it being then at 
Washington 8h. 17m. a.m. The eclipse ends on the earth in mid-ocean, in long. 
53° 18' 18" E. of Washington, in lat. 4° 24' 54" N., at sunset there, it being then 2h. 
3m. 36 sec. p.m. at Washington. The central eclipse begins in lat. 47° 11' 12" N., 
long. 45° 47' 24" W. of Washington, at sunrise there, and passes southeasterly- 
through Kansas, Missouri, Tennessee, Alabama, and Georgia, entering the ocean 
near Savannah,, and ends finally in Africa in lat. 16° 45' 54" N., long. 290° T west of 
Washington. The eclipse will be visible wherever the dark ground in the engrav- 
ing is seen, but as an annular eclipse only along the central line— each side of which 
it will be partial, the magnitude of the partial eclipse being smaller the farther we 
go from that line. 



zon at the instant of contact ; hence, the eclipse begins at local sun- 
rise. As the shadow system sweeps eastward, other elements of the 
penumbral cone become tangent to the earth's surface in succession, 
and the points of contact thus determined make up the curve along 
which the eclipse begins at sunrise. This curve, whose concavity is 
turned toward the west, in consequence of the earth's rotation, termi- 



184 ASTRONOMY. 

nates at the points which are determined by the two elements of the 
penumbral cone that lie in the central plane. 

That part of the central plane which lies within the penumbral cone 
(and which may be regarded as made up of elements radiating from 
the vertex) contains all the points from which the middle of the eclipse 
can be seen. When this plane strikes the earth the point of contact is 
a point from which the middle of the eclipse is seen at sunrise ; as it 
moves eastward its successive elements become tangent to the earth, 
and their points of contact make up the line which is marked on the 
map middle of eclipse at sunrise. In consequence of the earth's rota- 
tion this line lies to the westward of that along which the eclipse be- 
gins at sunrise, except at its extremities, which, for reasons already 
given, are identical with it. 

As the shadow system moves on, the elements of the following part 
of the penumbral cone become successively tangent to the earth, and 
their points of contact make up the line which is marked on the map 
eclipse ends at sunrise. This curve lies to the westward of both 
the others, except at its extremities, where it coincides with them. 
Within the looped space included by the first and the last of the lines 
just described is a region within which the sun rises partially eclipsed. 

As the moon's penumbra continues its eastward motion, the preced- 
ing part, by its intersection with the earth, determines the successive 
places at which the eclipse is just bcgiuning, the central plane deter- 
mines the places at which the middle of the eclipse is visible, and 
the following part determines the places where the eclipse is just 
ending. 

In passing off from the earth the preceding part determines a suc- 
cession of points which make up the line marked eclipse begins at 
sunset ; the central plane determines the points that constitute the line 
marked middle of eclipse at sunset; and the following part deter- 
mines the line marked eclipse ends at sunset. The point at which 
the shadow finally leaves the earth is the point which is marked last 
contact. The looped space bounded by the first and third of these 
curves contains all the places at which the sun sets partially eclipsed. 

When the line of centres of the sun and moon strikes the earth 
the central eclipse begins ; the intersection of this line with the 
earth's surface is the path of the central eclipse ; and when this line 
again becomes tangent to the earth the central eclipse ends. The 
intersection of the second nappe of the moon's umbra with the earth 
determines a zone along which the annular eclipse is visible. This 
zone is represented by the broad white line on the chart marked cen- 
tral. Had the eclipse been total a similar zone corresponding to the 



ECLIPSES. 185 

intersection of the moon's umbra with the earth would have marked 
the zone from which the total phase would have been visible. 

Observers to the northward of this zone see a partial eclipse on the 
sun's southern limb, and observers to south of it see a partial eclipse 
on the sun's northern limb, the magnitude in each case diminishing as 
the observer is situated nearer to the lines marked northern line of 
simple contact and southern limit. 

Greatest Duration of a Total Eclipse. 

143. The period of total obscuration at a given place is 
the time that it takes the moon's umbra to pass over that 
place. In order that this time may be as great as possible, 
the observer should be on the central line, the breadth of 
the moon's shadow should be as great as possible, and its 
relative motion with respect to the observer should be as 
small as possible. 

We have already seen that the breadth of the shadow will 
be as great as possible when the sun is at his greatest and 
the moon at her least distance from the earth. Further- 
more, the relative velocity of the shadow will be as small as 
possible when it travels through the equatorial region, and 
nearly parallel to the equator, for in that case the observer 
is carried eastward by the earth's rotation nearly half as fast 
as the shadow travels in the same direction. Hence, the 
duration of totality is greatest when the eclipse happens in 
summer, the moon being at that time near perigee and the 
central line being near the equator. Under favorable cir- 
cumstances the length of totality at a given place may 
amount to nearly 7 minutes. 

Phenomena Observed. 

144. A total solar eclipse at any particular locality is so 
rare an event that comparatively few people ever see one. 
Halley, in speaking of one that was visible in London in 
1715, says it was the first one that had happened at that 
place since 1140, an interval of 575 years. 



186 ASTRONOMY. 

The phenomena presented during the short period of 
totality are regarded as of so much importance, that astron- 
omers often take long journeys, at great expense of time 
and money, for the purpose of observing them. Indeed, 
almost every total eclipse that occurs in any part of the 
world is now carefully observed by well-equipped parties of 
scientific men scattered all along its path. 

Some of the phenomena observed are of special interest 
to the solar physicist, while others, if less important in 
this respect, are equally interesting to the student of gen- 
eral science. The appearances presented at different eclipses, 
and sometimes during the same eclipse at different places, 
are so various as to render it difficult to give a description 
of them all. Appearances that are clearly marked at one 
time are either not presented at all, or else pass unnoticed, 
at another. Some of these differences may undoubtedly be 
accounted for by varying atmospheric conditions, possibly 
some may be due to a variation in the character of the 
phenomena themselves, and not unlikely some arise from 
the peculiar temperaments of the observers. The most 
important phenomena generally observed are embraced in 
the following summary. 

Some time before the sun disappears, the atmosphere 
begins to grow gloomy and the shadows of trees are 
strangely mingled with crescent-shaped images of the wan- 
ing sun formed by rays penetrating the intervals between 
their leaves. As the time of complete obscuration ap- 
proaches, the aspect of the heavens undergoes a change; 
the sky assumes a lurid leaden hue which seems to be dif- 
fused over ail terrestrial objects ; the faces of the observers 
take on a cadaverous ashy tint ; birds seek their perches 
and animals their usual places of rest ; and a general feel- 
ing of uneasiness, like that which precedes impending 
calamity, seizes upon the minds of men. Then, the moon's 
umbra is seen approaching like a " wall of darkness ; " the 
last trace of the sun's thin crescent breaks up into shining 



ECLIPSES. 18? 

bead-like points and disappears; and the observer, plunged 
suddenly into an unnatural but not intense darkness, sees 
instead of the sun a black globe surrounded by a silvery 
coronal halo, broken here and there by the projecting flame- 
like protuberances of the sun's chromosphere. For a few 
fleeting minutes the brighter stars and planets appear, and 
then the glittering points of the chromosphere show them- 
selves on the other side of the moon ; the thin sickle of the 
solar disk begins to form ; the moon's umbra is seen sweep- 
ing away along its path ; and the observer is returned to 
daylight more suddenly even than he was plunged into 
darkness. 

Mr. Lockyer, in speaking of the beginning of totality, 
says: "One seems in a new world — a world filled with aw- 
ful sights and strange forebodings, and in which stillness 
and sadness reign supreme ; the voice of man and the cries 
of animals are hushed; the clouds are full of threatenings 
and put on unearthly hues ; dusky, livid, or purple, or yel- 
lowish crimson tones chase each other over the sky irrespec- 
tive of the clouds. The very sea is responsive and turns 
lurid red. All at once the moon's shadow comes sweeping 
over air, and earth, and sky, with frightful speed. Men 
look at each other and behold, as it were, corpses, and the 
sun's light is lost." 

The brilliant points seen at the instants of disappearance 
and reappearance of the sun's disk are called Baily's beads, 
being so named from the astronomer who first described their 
appearance ; in his description he speaks of them as "a row 
of lucid points, like a string of bright beads." The beads 
disappear suddenly at the commencement of totality, and 
reappear on the other side with equal suddenness at the end 
of totality. They have been accounted for by supposing 
that the solar crescent, when it consists of a mere thread of 
the chromosphere, is cut into segments by projections of the 
serrated edge of the moon ; these brilliant segments, contin- 
ually changing in form, are seen for an instant shining 



188 ASTRONOMY. 

through the lunar valleys. The different appearances of the 
beads at different times would seem to be dependent upon the 
degree of roughness of that part of the moon's surface which 
happens to form the edge of the lunar disk, and perhaps 
also upon slight variations in the apparent semi-diameters 
of the sun and moon at different eclipses. 

The corona, which has already been described, is by far 
the most important of all the phenomena manifested dur- 
ing a total eclipse, and for this reason we subjoin the fol- 
lowing additional description of it as given by Lockyer. 
After speaking of other appearances observed during the 
eclipse of 1871 in India, he says: "* * * there in the 
leaden colored, utterly cloudless sky shone out the eclipsed 
sun ! a worthy sight for gods and men. There, rigid in the 
heavens, was what struck everybody as a decoration, one 
that emperors might fight for, a thousand times more bril- 
liant even than the the Star of India, where we then were ! 
a picture of surpassing loveliness, and giving one an idea 
of serenity among all the activity that was going on below ; 
shining with the sheen of silver essence ; built up of rays 
almost symmetrically arranged round a bright ring above 
and below, with a marked absence of them to the right and 
left, the rays being composed of radial lines, separated by 
furrows of markedly less brilliance." 

Lunar Eclipses. Lunar Ecliptic Limits. 

145. Whenever, at the time of opposition, any part of 
the moon enters the earth's umbra there is a lunar eclipse, 
which may be either partial or total; it is partial when 
only a part of the moon enters the umbra, and it is total 
when the entire moon enters the umbra. 

In passing through the earth's penumbra, the light of the 
moon is but slightly dimmed, no more, perhaps, than it 
would be by an intervening haze. This dimming or partial 
obscuration is not usually regarded as an eclipse. 

The occurrence or non-occurrence of a lunar eclipse at 



ECLIPSES. 189 

the time of any full moon will depend upon the relative 
distances of the sun and moon and upon the position of the 
latter in her orbit. 

It has been shown by calculation that a lunar eclipse is 
impossible when, at the time of opposition, the sun is more 
than 12° from the moon's node, and that an eclipse is cer- 
tain when this distance is less than 9°. These angular dis- 
tances are called the lunar ecliptic limits. When the 
sun's distance from the node lies between these limits the 
occurrence or non-occurrence of an eclipse must be deter- 
mined by computation. 

The ecliptic limits corresponding to a total lunar eclipse 
are 5°.6 and 4°. 

The circumstances of a lunar eclipse which are predicted 
by astronomers and laid down in the almanacs are the times 
of beginning, of the middle, and of ending, and in case of 
a total eclipse the times of beginning and ending of the total 
phase ; in case of a partial eclipse the magnitude also is given. 

The circumstances of a partial lunar eclipse are illustrated 
by Fig. 85a. 




Fig. 85a. Partial Eclipse of the Moon. 

Explanation. NL is an arc of the ecliptic ; ND is the relative orhit of the 
moon ; KGB is the cross-section of the earth's umbra at the moon's distance from 
the earth ; C, E, D, are the positions of the moon at the times of beginning, middle, 
and end of the eclipse ; and AB, expressed in terms of the diameter of the moon, is 
the magnitude of the eclipse. In this case the moon is eclipsed on its southern 
limb, - 



190 ASTRONOMY. 

Extent of Visibility of Eclipses. 

146. A solar eclipse, being simply an occupation, or hid- 
ing, of the whole or a part of the sun by the intervening 
moon, is visible only at those places which are swept over 
by the moon's shadow system, and under the most favorable 
circumstances the area from which it can be seen is only a 
portion of a hemisphere. 

In a lunar eclipse, however, the whole or a part of the 
moon actually ceases to shine because its light is cut off by 
the intervening earth ; hence, the eclipse is visible over the 
entire hemisphere which is turned toward the moon. 

In consequence of the earth's rotation on her axis, the 
hemisphere which is turned toward the moon is continually 
changing, the eastern part passing out of the field of visi- 
bility and a new part from the west coming in. Hence, in an 
eclipse of long duration (and a total eclipse is sometimes 
visible for nearly two hours), some part of the eclipse may 
be seen over a region much greater than a hemisphere. 

As we shall see hereafter, solar eclipses are more numer- 
ous than lunar ones, but on account of the greater area over 
which the latter can be seen the number of lunar eclipses 
visible at any given place is much greater than the number 
of solar ones. 

Color of the Moon in Eclipse. 

147. During the time of a lunar eclipse the moon with 
all its markings remains visible, shining with a dull red or 
copper color, even during the time of totality. This phe- 
nomenon is due to the action of the earth's atmosphere on 
the solar rays that pass through its lower strata. In enter- 
ing our atmosphere these rays are bent toward the earth by 
more than half a degree, and at the same time they take on 
a reddish hue in consequence of the . absorption of their 
more refrangible elements ; in passing out of the atmos- 
phere, on their way to the moon, they are still further re- 
fracted and also undergo a still further absorption. The 



ECLIPSES. 191 

total bending, which may amount to more than a degree, is 
sufficient to throw them within the earth's umbra, and the 
total absorption is sufficient to produce the reddish color 
that we observe on the moon's disk. 

The depth of the color depends on the state of the at- 
mosphere along the circle in which the umbral cone is tan- 
gent to the earth, and the distinctness with which it is seen 
depends on the state of the atmosphere at the place of ob- 
servation. It is only in rare instances that the moon is 
completely invisible during the time of totality. When 
such cases occur the eclipsed moon is usually very near the 
horizon of the observer. 

Eclipse Seasons. 

148. If we suppose the sun to set out from one of the 
moon's nodes, traveling eastward at the rate of 360° a year, 
while the node itself is traveling westward at the rate of 
nearly 20° a year, the two will meet after an interval of 
346.62 days (Art. 110) ; hence, the sun's average daily mo- 
tion with respect to the node is nearly 1°.04, at which rate 
he would traverse the greatest solar ecliptic limit in about 
17.9 days, and the greatest lunar ecliptic limit in about 11.5 
days. We see, therefore, that no eclipse, either solar or 
lunar, can take place more than 18 days from the time 
of the sun's passing one of the moon's nodes, either be- 
fore or after. For this reason we call the period made up 
of 18 days before the sun reaches either node and of 18 days 
after he passes that node an eclipse season. Inasmuch 
as it takes the sun 173.31 days to pass from either node to 
the one opposite, the interval between the end of one eclipse 
season and the beginning of the next is a little more than 
137 days. 

Number of Eclipses in an Eclipse Season. 

149. The number of eclipses that may occur in a single 
eclipse season depends upon the ecliptic limits and also 



192 ASTRONOMY. 

upon the position of the sun at the times of full and new 
moon. 

The average value of the solar ecliptic limits is 161°, and 
that of the lunar ecliptic limits is 10^°; if we regard 1°.04 
as the average daily motion of the sun with respect to the 
node, the former distance will correspond to 16.1 days, and 
the latter distance to 10.1 days ; hence, we say that there will 
probably be a solar eclipse when new moon happens within 
16 days of the node on either side, and a lunar eclipse when 
full moon occurs within 10 days of the node on either side. 

There may be three eclipses in one eclipse season ; for, if 
we suppose full moon to happen within 1 day of the node, 
there will be a lunar eclipse at that time, and furthermore, 
the new moon that occurs 14.8 days before, and also the 
new moon that takes place 14.8 days after, will both be 
within less than 16 days of the node, and consequently at 
each of these times there will probably be a solar eclipse. It 
is impossible to have two lunar eclipses in one season ; for, 
the interval between two full moons is 29.5 days; hence, if 
one falls within 11.5 days of the node, the other must hap- 
pen at a greater interval than 11.5 days from the node. We 
see therefore that when there are three eclipses, one must 
be lunar and two solar. In this case it is to be noted that 
the lunar eclipse will be total, both of the solar eclipses 
being partial. 

It may happen that there will be but one eclipse in a 
season; for if we suppose new moon to happen within 1 
day of the node, there will be a central solar eclipse at that 
time, and inasmuch as the full moon that occurs 14.8 days 
before, and. the full moon that takes place 14.8 days after, 
are each more than 11.5 days from the node, there will 
probably be no lunar eclipse at either of these times. 

It is easily seen that in most cases there will be two 
eclipses in a season, one of which will be lunar and the 
other solar. 

Flammarion, in his Popular Astronomy, gives the details 



ECLIPSES. 193 

of all the eclipses that have happened and that will happen 
from the beginning of 1880 to the end of 1900. If we take 
a cycle of 38 eclipse seasons, beginning with December 1, 
1880, we find that 4 of these seasons embrace 3 eclipses 
each, 12 contain but 1 each, and 22 contain 2 each, the 
whole number in the cycle being 68. 

The average number of eclipses in a calendar year is 
nearly 3f , that is, there will be at the rate of 15 eclipses in 
4 years. It is theoretically possible that 7 eclipses may oc- 
cur in a single year, and it is absolutely impossible that 
there should be less than 2; of the 21 years above referred 
to, 1 year has 6 eclipses, 5 years have 5 each, 8 years have 
4 each, 1 year has 3, and 6 years have 2 each. 



The Eclipse Cycle, or the Saros. 

150. The time that it takes for the sun to revolve from 
one of the moon's nodes around to the same node again is 
346.62 days, and the time of 19 such revolutions is 6585.78 
days; the average length of the moon's synodical revolu- 
tion is 29.53058 days, and the length of 223 such revolu- 
tions is 6585.32 days ; hence, a period of 223 lunar months 
falls short of 19 nodical revolutions of the sun by .46 of a 
day, in which time the sun's motion with respect to the 
node is less than half of a degree. 

Furthermore, 223 lunations correspond almost exactly to 
two revolutions of the line of apsides with respect to the 
node. Hence, at the end of a period of 223 lunar months 
the sun and the moon will have returned very nearly to 
the same positions with respect to the moon's orbit that 
they had at the beginning of it, and consequently the 
eclipses of that period will be repeated in the same order 
and with but little variation in magnitude. This period of 
6585.32 days is an eclipse cycle ; it is equal to 18 years 
and 10| or 1:L i days, according to the number of times that 
9 



194 ASTRONOMY. 

the cycle contains the 29th day of February ; it was known 
to the ancients, by whom it was called the Saros. 

If we have the date of the middle of any eclipse we can 
find the date of its return to a very close degree of approx- 
imation, by adding 6585.32 days. The following illustra- 
tion showing the times of recurrence of a total eclipse, and 
the regions in which the central eclipse is visible in each 
case, is copied from Newcomb's Popular Astronomy : 

1850, August 7th, 4h. 4m. p. m., in the Pacific Ocean ; 

1868, August 17th, 12h. p. M., in India; 

1886, August 29, 8h. a.m., in Central Atlantic and S. 
Africa ; 

1904, September 9th, at noon, in South America. 
It will be seen that the region in which the central phase 
is visible at each return shifts toward the west by a distance 
nearly equal to one-third of the earth's circumference : this 
change is due to the fact that the interval between two 
successive returns exceeds an integral number of days by 
nearly 8 hours. 

It is to be noted that there is a slight difference in phase 
of an eclipse at its successive recurrences ; for the place of 
the sun with respect to the node is .46 of a day further to 
the west at each return. In consequence of this slight 
change, new eclipses gradually come into the cycle from the 
east and old ones leave it on the west. The average time 
that a lunar eclipse remains in the cycle is something more 
than 800 years, and the time that a solar eclipse remains 
is more than 1200 years. 

The following account of the changes that may occur in 
an eclipse at successive returns is taken from Chambers' 
Descriptive Astronomy. In speaking of a solar eclipse 
which appeared at the north pole in June, 1295, and which 
moved southward at each return, he says : " On August 
27, 1367, it made its first appearance in the north of 
Europe ; in 1439 it was visible all over Europe; at its 19th 
appearance, in 1601, it was central in London ; on May 5, 



ECLIPSES. 195 

1818, it was visible at London; and was again nearly cen- 
tral- at that place on May 15, 1836. At its 39th appearance, 
August 10, 1980, the moon's shadow will have passed the 
equator, and, as the eclipse will take place near midnight, 
it will be invisible in Europe, Africa, and Asia. At every 
subsequent period the eclipse will go more and more to- 
ward the south, until finally, at its 78th appearance in Sep- 
tember 30, 2665, it will go off at the south pole of the earth, 
and disappear altogether." 

In the cycle of eclipses which includes the 1st of Decem- 
ber, 1880, and extends to the 12th of December, 1898, there 
-are 68 eclipses, of which 42 are solar and 26 lunar ; that is, 
the numbers of solar and lunar eclipses are very nearly 
proportional to the average values of the solar and lunar 
ecliptic limits. 

Of the solar eclipses in this cycle, 15 are partial, 12 are 
total, and 15 are annular; of the lunar eclipses 15 are par- 
tial and 11 are total. 



Occultations. 

151. When one celestial body is hidden from view by 
the interposition of another, the phenomenon is called an 
occultation. According to this definition a total eclipse 
of the sun would be called an occultation, but astronomical 
usage has made the term technical, and it is now restricted 
almost entirely to the phenomenon of the moon's passage 
over a star or planet. 

As the moon advances from west to east it sweeps over a 
belt of the heavens whose breadth is about half a degree, and 
every star in that belt must be occulted as the moon passes 
over it. When a star is occulted it disappears at the eastern 
or advancing limb of the moon, and reappears at the west- 
ern or following limb ; the instant of its disappearance is the 
time of immersion, and the instant of its reappearance 
is the time of emersion. 



196 ASTKONOMY. 

It is difficult to observe either phase, even in the case of a 
bright star, except at the moon's dark limb. During the first 
half of a lunar month the dark limb is turned toward the 
east, and during the last half it is turned toward the west; 
hence, times of immersion are usually observed between 
new moon and full, and times of emersion between full 
moon and new, the most favorable times in both cases 
being near new moon. 

Occultations are usually observed for the purpose of de- 
termining the longitude of the place of the observer. To 
aid him, a list of stars liable to occultation is given in the 
Astronomical Ephemeris, together with certain data in- 
tended to facilitate computation. When the observed time, 
either of immersion or emersion, is known, the local time of 
conjunction of the moon and star as seen from the centre 
of the earth can be calculated ; the Greenwich time of this 
conjunction can be found from the ephemeris; then, the 
difference of these times is the observer's longitude from 
Greenwich. 



VIII. OF TIDES. 

Definitions. 

152. Tides are periodical elevations and depressions of 
the surface of the ocean ; as a general rule the waters rise 
for about six hours, and fall for an equal time, remaining 
stationary for a short interval at each turn of the tide. 
The rising of the waters is called flood tide, their falling 
is called ebb tide, and during the intermediate intervals 
it is said to be slack water. The average time required 
for a tide to pass through all its phases is 12h. 25m., or half 
a lunar day. 

Causes of Tides. 

153, The tides are caused by the inequality of attraction 
exerted by the moon, and also of the sun, upon opposite 
sides of the earth. 

To explain the manner in which these causes operate to 
produce tides, let us first consider the action of the moon 
alone. 



■e 



Fig. 86. Popular Illustration of the Cause of the Tides. 

Explanation. In Fig. 86 let M be the centre of the moon, E the centre of the 
earth, FDCG a section of the earth by any plane through M and E, DC the diameter 
whose direction passes through M, FG any chord whose direction passes through 
M, and which is therefore nearly parallel to DC, and H a point of FG whose distance 
from M is equal to ME. 



198 ASTRONOMY. 

Suppose C, E, and D to be three equal particles; then, 
from the Newtonian law, the moon's attraction on C will 
be greater than it is on E, and her attraction on E will be 
greater than it is on D ; hence, will be drawn away from 
E, and E away from D, or what is the same thing relatively, 
the action of the moon is to draw both and D away from 
the centre E. Again, let Gr, H, and F be three equal parti- 
cles; then it may be shown as before that the action of the 
moon is to draw both G and F away from H. The total 
effect of the moon's attraction is therefore to draw all the 
particles on the side CG- toward M, and all the particles on 
the opposite side FD, away from M, this effect being great- 
est near and D, as shown by the arrow-heads in the figure. 

If the earth were at rest, these forces would produce two 
broad protuberances, one having its apex at C, directly 
under the moon, and the other having its apex at D, dia- 
metrically opposite ; but before these protuberances have 
time to form, the earth turns on its axis so as to bring new 
points under the moon, at which the tendency to form the 
protuberances is renewed, and so on continually. The re- 
sult of this continued action is the formation of two broad 
flat waves, called tidal waves, which follow the moon in 
its diurnal motion, moving from west to east around the 
globe. 

In what precedes we have supposed the entire earth to be 
covered by water, whereas in reality the ocean is interrupted 
by continents, islands, and shoals, which break up and 
greatly modify the continuity of the tidal waves, without 
destroying them. 

The action of the sun upon the waters of the globe is 
similar in hind to that of the moon, but inasmuch as its 
inequality of attraction on opposite sides of the earth is 
much smaller, its tide-producing power is less than that of 
the moon in the ratio of 4 to 9. It might be expected that 
the sun would form two independent tidal waves, but in- 
stead of this the sun and moon conspire to produce two 



OF TIDES. 199 

resultant waves lying on opposite sides of the earth, of 
which the heights and, in some degree, the positions are 
dependent upon the relative positions of these two bodies. 

The resultant wave, whose crest is on the side of the 
earth turned toward the moon, is called the Tipper tide 
wave, and the one that is on the opposite side of the earth 
is the lower tide wave. When either wave is approach- 
ing a place it is flood tide, when the crest of the wave 
reaches the place it is high water, and whilst the wave is 
receding it is ebb tide. In explaining the law of distribu- 
tion of tides it wnll generally be sufficient to consider the 
upper wave only, for what is said of it will be equally true 
of the lower one. 

Distribution of Tides. 

154. If the entire earth were surrounded by a deep ocean, 
the crest of the tide-wave would lie nearly north and south ; 
following the westward motion of the moon in her diurnal 
path, it would move regularly around the earth in a lunar 
day, its velocity in the equatorial regions being about 1000 
miles an hour ; the tides would be highest near the equator, 
and would gradually diminish in altitude toward the poles, 
where they would be insignificant. 

In consequence, however, of the peculiar arrangement of 
the land and water of the globe, this simple law is greatly 
changed, so that the actual law of distribution of the tides 
is exceedingly complex. And yet, in spite of this complex- 
ity, there is at each place on the earth so great a regularity 
in the times and heights of the tides that both may be pre- 
dicted with sufficient precision for all practical purposes. 

It is found by observation that all the principal tides of 
the world depend on a great primal wave, which is de- 
veloped by the direct action of the sun and moon on the 
vast expanse of water in the southern Pacific Ocean. The 
general course of this wave is westward, but as it advances 
it sends off branches, first into the northern Pacific, then 



200 ASTROHOMY. 

into the Indian Ocean, and finally into the Atlantic, being 
everywhere reinforced and sustained by the minor tide- 
waves that are generated in those oceans. 

The branch sent into the northern Pacific moves rapidly 
along the deep waters, and more slowly in the shallower 
waters of that ocean, and at the end of 10 or 12 hours 
reaches the eastern shores of northern Asia and the western 
shores of North America. 

The main wave, after being delayed by shoals and islands, 
reaches the waters of southwestern Australia about half a 
lunar day after its generation, that is to^say, when it is 
about half a day old. Sending a branch northward, which 
goes to produce the tides of the Indian Ocean, the main 
wave reaches the South Atlantic at the Cape of Good Hope 
after another half of a lunar day. Here it is deflected 
northward by the opposing continent of America, reaching 
the middle of the North Atlantic when it is about 37 hours 
old. 

When the wave first enters the Atlantic Ocean, its crest 
has a. curved form, whose convexity is turned toward the 
northwest ; as it moves on, the curve that marks the ad- 
vancing crest becomes more convex, the vertex of the curve 
following the general line of the deepest water ; when it 
reaches the middle of the North Atlantic the crest has 
taken a parabolic form, whose axis is directed northward, 
whose western side is nearly parallel to the general trend of 
the eastern coast of the United States, and whose eastern 
side is nearly parallel to the coast line of the Eastern Conti- 
nent. The western portion of the wave falling upon the 
coast of the United States, gives us our tides, the eastern 
portions produce the tides of southwestern Europe, and the 
still advancing front, after sending off branches to the east 
and west, finally loses itself in the Arctic Ocean. 

It will be seen that the wave which produces the tides of 
the eastern coast of the United States is something more 
than 1J lunar days old when it reaches us; hence, the tides 



OF TIDES. 201 

that we get are not due to the last transit of the moon, ex- 
cept so far as they are reinforced by the local tide-wave gen- 
erated in the Northern Atlantic, but to the action of the 
sun and moon nearly 40 hours before. The tides at London, 
which reach that place by a wave that passes around to 
north of Scotland, and then down the North Sea, take 
place nearly 2| days later than the genesis of the primal 
wave in the Pacific Ocean. 

Spring and Neap Tides. 

155. The heights of the tides at any place depend upon 
the relative positions of the sun and moon. When these 
bodies are in conjunction or in opposition, that is, at the 
times of neiv moon and of full moon, they both tend to pro- 
duce high water at the same time. This gives rise to the 
highest tides, which are called spring tides. When the 
sun and moon are 90° apart, that is, at the times of the first 
and of the third quarter of the moon, the sun acts to pro- 
duce high water at the same time that the moon acts to 
produce low water, and the reverse ; this gives rise to the 
lowest tides, which are called neap tides. 

In consequence of the retardation of the primal wave, as 
explained in the preceding article, the spring tides on our 
coast do not occur till the third or fourth tide after new 
or full moon, nor do the neap tides happen till an equal 
interval after the first and third quarters of the moon. 

Variations due to the Distances of the Sun and Moon. 

156. It has been found by computation that the tide- 
producing powers of the sun and of the moon, when both 
are at their mean distances from the earth, are to each other 
very nearly as 4 to 9. If we represent the corresponding 
height of the solar tide by 1, that of the lunar tide will be 
represented by 2.25 ; on the same scale, the height of 
neap tide will be represented by 1.25 and that of spring tide 



202 ASTRONOMY. 

by 3.25, that is, the average height of neap tide is to that 
of spring tide as 5 is to 13. 

The relations between the heights of the tides, both solar 
and lunar, undergo considerable variations on account of 
the varying distances of the sun and moon from the earth. 
It has been shown by the higher analysis that the tide- 
producing power of either of these bodies varies inversely as 
the cube of its distance from the earth. 

By means of this principle, we can show that the heights 
of the lunar tides corresponding to the moon's greatest, 
mean, and least distances, are to each other as the numbers 
85, 100, and 117. On the scale adopted, the heights of the 
corresponding lunar tides are represented by the numbers 
1.91, 2.25, and 2.63. It may also be shown that the heights 
of the solar tides corresponding to the sun's greatest, mean, 
and least distances, are proportional to the numbers 95, 
100, and 105. On the scale adopted, the heights of the 
corresponding solar tides are represented by the numbers 
.95, 1, and 1.05. 

The highest possible spring tide will occur when the 
moon is in perigee and the earth in perihelion ; on the scale 
adopted it will therefore be denoted by the number 3.68. 
The lowest possible neap tide will happen when the moon is 
in apogee and the earth in perihelion ; it will be represented 
by the number .86. These results indicate the greatest 
possible range of the tides measured at open sea. 

The tides that occur when the moon is in perigee are 
called perigean tides, and those that occur when the moon 
is in apogee are called apogean tides. If we consider the 
sun at his mean distance, the greatest apogean will be to the 
greatest perigean tide as 291 is to 363. 

The Diurnal Inequality. 

157. We have seen that the combined action of the sun 
and moon gives rise to a single upper and to a single lower 



OF TIDES. 203 

tide; we have also seen that the vertices of these tides tend 
to conform to the position of the moon rather than to that 
of the sun ; consequently the vertex of the upper tide is 
generally on the same side of the equator as the moon and 
that of the lower one is on the opposite side, or what is the 
same thing, the vertices of the two tides cross the meridian 
of any place at unequal distances from that place. But the 
height of the tide at any place depends upon the distance 
of the place from the apex of the corresponding tide- wave ; 
hence, there is a difference between the heights of the upper 
and lower tides at any place, which difference is called the 
diurnal inequality. 

The diurnal inequality is dependent principally on the 
declination of the moon, but somewhat also on the sun's 
declination ; it is greatest when both the sun and the moon 
are farthest north or farthest south, and it totally disappears 
when both are in the plane of the equator. 

On the eastern coast of the United States, where the tides 
arrive by a circuitous route, the diurnal inequality is so 
modified as to be quite inconspicuous ; but on the western 
coast, where the tides are received more directly, it is a 
marked feature of the alternating tides. Thus, in the port 
of San Francisco, when the moon has its greatest declina- 
tion, the range of the higher tide is nearly 7 feet, and the 
range of the lower one varies from 1|- to 3 feet ; on the 
Atlantic Coast the greatest value of the diurnal inequality 
is less than 1 foot. 



Priming and Lagging of the Tides. 

158. The combined action of the sun and moon tends at 
each instant to produce a tide-wave whose vertex, as seen 
from the centre of the earth, lies between the two bodies 
and nearer the latter. The interval between two successive 
passages of this wave over the meridian of any place, which 
is the same as the interval between two successive upper 



204 ASTRONOMY. 

tides at that place, is called a tidal day. In the course 
of each synodic revolution the average length of a tidal day 
is the same as that of a lunar day ; but on account of the 
varying angular distance of the moon from the sun, the 
position of the tidal wave with respect to these bodies is 
continually changing, and consequently the actual lengths 
of different tidal days are unequal. 

At the time of the moon's conjunction with the sun the 
vertex of the tide-wave is supposed to be directly under the 
moon. Setting out from this time, the tide-wave continually 
falls behind, that is, to the westward of the moon, until the 
end of the first quarter, when the total retardation becomes 
a maximum ; during this interval the average length of the 
tidal day is less than that of a lunar day. At the beginning 
of the second quarter the tidal-wave begins to gain on the 
moon, and continues to gain until the end of the second 
quarter, at which time the upper tide of the moon will 
coincide with the lower tide of the sun : during this period 
the average length of the tidal day is somewhat greater 
than a lunar day. 

Setting out again from the time of full moon, and re- 
membering that we are now comparing the position of the 
upper lunar with the lower solar tide, we find as before 
that the average tidal day during the third quarter is 
shorter, and during the fourth quarter longer than a lunar 
day. Hence, during the first and third quarters the time 
of high water is accelerated, and during the second and 
fourth quarters it is retarded: the acceleration is called 
priming, and the retardation is called lagging. 

As an illustration we may state that the average time of 
high water at Montauk Point, L. I., is 8h. 20m. after the 
transit of the moon ; but in consequence of pri7ning it may 
happen as early as 7h. 50m. after the time of transit, or in 
consequence of lagging it may not occur till 8h. 50m. after 
the time of transit, or the time of southing of the moon, as 
it is called in the almanacs. 



OF TIDES. 



205 



Establishment of a Port. 

159. The mean interval between the moon's transit 
across the meridian and the time of the following high 
water at any port, taken on the clays of new and full moon, 
is called the establishment of the port. This is the 
common establishment, and is given in books on navigation 
and laid down on charts. The average of all the intervals 
between the times of transit of the moon and the following 
times of high water, during a month, is known as the 
mean or corrected establishment. It is this establish- 
ment which is given in the Coast Survey reports, and laid 
down on the Coast Survey charts. 

When w r e know the establishment of a port and the range 
of priming and lagging, we' can form a pretty close estimate 
of the time of high water at that port. The time of the 
moon's transit can be found with sufficient accuracy from 
a common almanac. 

We subjoin a short table compiled from a Coast Survey 
report. In the first column is the name of the port ; in the 
second column is the establishment ; in the third, is the ex- 
treme range of the variation from the establishment ; in the 
fourth, the mean height of high above low water ; in the 
fifth, is the height of spring tides ; and in the sixth, is the 
height of neap tides. 

TABLE. 



1. 


2. 


3. 


4. 


5. 

20.6ft. 

9.9ft. 
11.3ft, 
5.6ft. 
5.4ft. 
6.8ft. 
6.0ft. 
7 6ft 


6. 


Eastport, Me 

Portsmouth, N. H 

Boston, Mass 


llh. 8m. 
llh. 23m. 
llh. 27m. 

7h. 29m. 

8h. 13m. 

Ih. 18m. 

7h. 26m. 

8h. 13m. 

9h. 38m. 

Ih. 14m. 


5 1 m. 

53m. 

43m. 

47m. 

43 m. 

44m. 

48m. 

51m. 
Hi. 35m. 
Ih. 15m. 


- 
18.1ft. 

8.6ft. 
10.0ft. 

4.8ft. 

4.3ft. 

6.0ft. 

5.1ft. 

6.5ft. 

3 7ft, 

4.8ft.. 


15.4ft. ! 
7.2ft. 
8.5ft. 
4.0ft, 
3.4ft, 
5.1ft. 
4.1ft. 
5 oft 


Sandy Hook, N. Y. . . . 

New York City 

Philadelphia, Pa 

Charleston, S. C 

Savannah, Cra 


San Diego, Cal 

San Francisco, Cal 

—_ 


5.0ft. 

5.2ft, 


23ft. 
4.1ft. 



206 ASTRONOMY. 



Modifications Due to the Form of a Coast. 

160. The tides at different places along an extended 
coast are greatly modified by the conformation of the shore 
line and by the manner in which the wave strikes it. 

When the crest of the advancing wave falls centrally upon 
a projecting cape, the two parts into which it is divided 
move along the sides of the cape, giving a comparatively 
small tide at the cape, and larger ones further on ; thus, 
the Atlantic wave when it falls upon Cape Hatteras gives a 
tide of only 2 feet at the cape, whilst those which, are 
produced both to the north and south of the cape are from 
4 to 6 feet in height. 

If the wave falls obliquely upon the cape, it is partially 
deflected so as ta produce a smaller tide behind the cape ; 
thus, the wave that moves up St. George's Channel in Great 
Britain is deflected by Carnsore Point in Ireland toward 
the opposite shore of Wales, where it produces large tides, 
while the tides on the eastern shore of Ireland are com- 
paratively small. 

When a bay or indentation of the coast presents a favor- 
able opening to the tidal wave, the tide becomes higher and 
higher from the mouth to the head of the bay. Prof. Hil- 
gard, in the Smithsonian report for 1874, says that this is 
due to the concentration of the wave by the approach of the 
shores and the gradual shoaling of the bottom. He illus- 
trates the law by referring to the tides of the Atlantic coast 
of the United States which, in general outline, is made up of 
three large bays : the great southern, from Cape Florida to 
Cape Hatteras; the great middle, from Cape Hatteras to 
Nantucket; and the great eastern, from Nantucket to Cape 
Sable. 

The Atlantic tide-wave arrives at about the same time at 
Cape Florida, Cape Hatteras, Nantucket, and Cape Sable, 
and at those points its height is inconsiderable compared 
with the rise at the heads of the several bays. At Cape 



OF TIDES. 207 

Florida the mean rise and fall is only 1} ft., and at Cape 
Hatteras only 2 ft., while at Savannah it reaches 7 ft. 
Again, at the head of the middle bay in New York harbor 
it reaches 5 ft., while at Nantucket it is bnt little greater 
than 1 ft. 

The configuration of the eastern bay is less regular, 
and the correspondence of heights is not so obvious. 
The recess of Massachusetts Bay is well marked, and the 
tides reach the height of 10 ft, at Boston and Plymouth. 
Boiling eastward along the coast of Maine, the tide contin- 
ually increases ; but the most striking effect of converging 
shores is exhibited in the bay of Fundy. At Eastport and 
St. John's the mean height of the tide is 19 ft,, but at Sack- 
ville, in Cumberland basin, it is 36 ft., attaining to 50 ft. 
or more at spring tides. 

In a similar manner we can explain the high tides at the 
head of Panama Bay in Central America, and in Bristol 
Channel in England. 



Effect of Depth on the Velocity and Height of Tide-Wave. 

161. We have seen that the great tide- wave moves over 
more than 70° of latitude in about 12 hours in its advance 
along the deep channel of the Atlantic Ocean. As it ap- 
proaches the coast its velocity is rapidly diminished, and 
when it enters our harbors and rivers, where the water is 
shoal, it is reduced to 20 or 30 miles an hour, and some- 
times to even less. 

The average velocity of the tide-wave flowing through 
Long Island Sound is but little more than 35 miles an 
hour ; in advancing from Sandy Hook to New York City 
it is only about 20 miles an hour; and in moving from 
New York, up the Hudson Eiver to Albany, it is not far 
from 16 miles an hour. In all of these cases the height of 
the tide tends to increase as the depth of water diminishes 
and the sides of the channel converge ; this tendency, how- 



208 ASTRONOMY. 

ever, is subject to the counteracting effect of friction and 
obstructions of various kinds. 

The effects of these changes of height and velocity are 
strikingly manifested in the tidal system of New York and 
its vicinity. The great Atlantic wave enters New York 
harbor at Sandy Hook about the same time that it enters the 
east end of Long Island Sound, and the two partial waves 
advance to meet each other in the neighborhood of Fort 
Schuyler. The wave that enters by Sandy Hook advances 
at first with a velocity of 20 miles an hour and with com- 
paratively little variation in height; on entering the East 
Eiver its velocity is rapidly reduced to about 7 miles an 
hour, and in consequence of the tortuosity of the channel 
its height is diminished rather than increased. 

The wave that enters the east end of the sound is at first 
less than 2 feet in height, but as it travels westward this 
height increases, being 6 feet at New Haven, and rising to 
over 7 feet when it reaches Throg's Neck. In consequence 
of the greater height of tide thus produced by the wave 
coming through the sound, a portion of the flood passes 
through the narrow channel below the place of meeting, 
giving rise to numerous irregular currents, and finally 
leaves New York harbor with the ebb, thus contributing 
to the scouring effect of the outgoing tide, and aiding to 
keep up the depth of channel necessary for the purposes 
of navigation. 

The tides of the North, or Hudson, River average about 
3i feet in height at Tarrytown, are less than 3 feet at West 
Point, and rise to 4 feet at Tivoli, from which place they 
diminish in altitude to Albany, where they are a little over 
2 J feet. The rate at which the tide-wave ascends the river 
is not far from the speed of the North Eiver steamboats ; 
hence, if a boat leaves New York at high water it has the 
benefit of the tidal current all the way to Albany. 

In many cases where the mouth of a river is at the head 
of a bay, and the waters are shoal in its vicinity, the in- 



or tides. 209 

coming wave is thrown into the form of a head or wall of 
ivater that has been named a bore, which ascends the 
river with great impetuosity. The tidal bore at Tsien-tang 
is said to extend across the river, and to be 30 feet high ; 
the tidal bore of the Hooghly, one of the mouths of the 
Ganges, is from 20 to 25 feet high ; and at the mouth of 
the Amazon it is 12 or 13 feet high. 

Tides of Inland Seas. 

162. In consequence of the narrowness of the entrance 
channels to the Mediterranean and the Baltic seas, their 
tides are very small. In the Mediterranean the average 
height of the tides is no more than If feet, although in 
some places they reach an altitude of 3 feet. 

In inland lakes the tides are so insignificant that they are 
almost entirely masked by other and greater irregularities. 
A few j^ears ago Gen. Graham made a long series of obser- 
vations on Lake Michigan, from which he inferred that the 
height of the tides on that body of water was less than 
2 inches. Hence, we may conclude that inland seas like 
the Caspian and the large lakes like those on our northern 
border are practically tideless. 



IX. OF CALENDARS. 

Definitions. 

163. A calendar is a register of epochs and periods of 
time arranged to meet the wants of civilized life. 

When arranged with reference to the needs of civil life it 
is a civil calendar ; when arranged to meet the demands 
of the church it is an ecclesiastical calendar. 

Natural and Artificial Units of Time. 

164. The natural units of time are the solar day, the 
lunar month, and the tropical year. 

The mean solar day is the average length of all the solar 
days in a year ; the mean lunar month is equal to 29.53058 
mean solar days ; and the mean tropical year is equal to 
365.2422 mean solar days. 

It will be seen that the lengths of natural months and 
the natural year are incommensurable with the day, which 
is the fundamental unit of time ; for this reason, the calen- 
dars now in use are constructed by combining artificial 
months and years as explained below. 

In the civil calendar each year is made up of 12 artificial 
months, called calendar months ; a calendar month may 
contain 28, 29, 30, or 31 days. 

The calendar years are of two kinds: common years, 
containing 365 days, and bissextile or leap years, con- 
taining 366 days ; these are so distributed that after a long 
period of time the average length of the calendar year shall 
be very nearly equal to that of the mean tropical year. 

In the ecclesiastical calendar the months employed are of 
two kinds: solid months, which contain 30 days each, 



OF CALENDARS. 211 

and hollow months, which contain 29 days each ; these 
are so distributed that after a long period of time their 
average length shall be very nearly equal to a mean lunar 
month. 

The week, though not an astronomical period, corres- 
ponds roughly to a quarter of a lunar month ; it is used 
both in the civil and in the ecclesiastical calendar. 

The order of arrangement of the Latin names of days is 
suggested by the following geometrical construction. 

» Explanation. The circumfer- 
ence of a circle is divided into 7 equal 
parts, and at each point the sign of a 
planet is placed, the order of succes- 
sion being the same as the order of 
their assumed distances from the 
earth regarded as the central body. 
The points are then joined by lines as 
shown in the diagram, thus forming 
a regular 7-pointed star polygon. 
Starting now from any planet, say 
the Sun, and following the directions " 

indicated by the arrows, we come in Fig. 87. Order of the Days of the 
succession to the Moon, Mars, Mer- Week. 
cury, Jupiter, Venus, Saturn, and 

thence back to the sun. This order is the same as the order of the 
days of the Roman week. 

The week, as a cycle of time, appears to have been intro- 
duced among the Eomans during the reign of the emperors. 
The names which the Eomans gave to the days of the week 
were derived from those of the seven bodies, which at that 
time were called planets, viz. : the Sun, the Moon, Mercury, 
Venus, Mars, Jupiter, and Saturn. These names, in being 
transmitted to us, were modified by our Saxon ancestors, 
who substituted Woden for Mercury, Friga for Venus, 
Tuisco for Mars, and Thor for Jupiter. The original 
names and their modifications are shown in the following 




212 



.2 


ASTRONOMY. 






TABLE. 




Latin names. 


Modified names. 


Present names. 


Dies Solis 


Sun's Daeg 


Sunday 


Dies Lunaa 


Moon's Daeg 


Monday 


Dies Martis 


Tuisco's Daeg 


Tuesday 


Dies Mercurii 


Woden's Daeg 


Wednesday 


Dies Jovis 


Thor's Daeg 


Thursday 


Dies Veneris 


Friga's Daeg 


Friday 


Dies Saturn i 


Saturn's Daeg 


Saturday. 



Origin of the Civil Calendar. 

165. Our civil calendar is based on that of the ancient 
Romans. It is said that Eomulus instituted a cycle of 304 
days, divided into 10 months, which were called Martins, 
Apr His, Mains, Junius, Quintilis, Sextilis, September, Oc- 
tober, November, and December. 

His successor, Numa Pompilius, added two months, 
called Januarius and Februarius, the former of which he 
placed at the beginning and the latter at the end of the 
Eomulian cycle. He arranged the lengths of the months 
so that the twelve should contain 355 days, which differs 
but 1 day from 12 lunar months. To adjust this to the 
tropical year, which is the cycle of the seasons, he directed 
that every second year should be increased by an additional 
month, called Mercedonius. This added month contained 
alternately 22 and 23 days, and was intercalated between 
the 23d and 24th of February, the former being the day 
set apart for the feast of Terminalia. The luni-solar year 
thus established was, on the average, about 1 day longer 
than the tropical year, a fact which soon led to a modifica- 
tion of the rule for intercalation, and ultimately to much 
irregularity in the calendar. 

Under the Decemviri the month of January was taken 
from the beginning of the year and placed between the 
months of December and February. The order of the 



OP CALENDARS. 213 

months and the number of days in each then stood as fol- 
lows: Martius, 31; Aprilis, 29; Mains, 31; Junius, 29; 
Quintilis, 31 ; Sextilis, 29; September, 29; October, 31; 
November, 29 ; December, 29; Januarius, 29; and Febru- 
arys, 28. The rule for intercalation at this time is some- 
what uncertain, though Scaliger, in speaking of the old 
Eoman luni-solar calendar, says that "the principle was 
to intercalate a month alternately of 22 and 23 days every 
other year during periods of 22 years, passing over the 
last biennium, so that in each period 10 such intercalary 
months were inserted.'" According to this rule the average 
year would approximate pretty closely to the year of the 
seasons ; but the rule was misapplied, and the calendar 
soon fell into great confusion. 

The Julian Reform. 

166. Acting on the advice of Sosi genes, an Alexandrian 
astronomer, Julius Caesar, made a radical reform in the 
calendar. He abolished the old lunar calendar, with its 
intercalary months, and substituted therefor a purely solar 
calendar. He changed the order of the months so as to make 
the year begin when the earth was in perihelion ; this was 
done by causing the year 45 B. C, which at that time began 
a little before the middle of October, to end on the last day 
of the second following December. This year, which was 
thus made to contain 445 days, is known by chronologists 
as the year of confusion. He assumed the length of the 
solar year to be 3 65 J days, and in order to take account of 
the fractional part of a day, he directed that the first three 
years of each quadrennium should contain 365 days, but 
that the fourth year should contain 366 days. The addi- 
tional day in every fourth year was intercalated in the place 
occupied by the old month Mercedonius, that is, between 
the 23d and the' 24th of February. 

He readjusted the lengths of the months, the name of 
the old month Quintilis being changed to Julius in honor 



214 ASTRONOMY. 

of the reformation. The names of the months and the 
number of days in each then stood as follows : Januarius, 
31 ; Februarius, 29 ; Martius, 31 ; Aprilis, 30 ; Maius, 31 ; 
Junius, 30 ; Julius, 31 ; Sextilis, 30 ; September, 31 ; Octo- 
ber, 30 ; November, 31 ; and December, 30. 

The Augustan Correction. 

167. In carrying out the orders of Julius Cassar, the rule 
for intercalating the additional day was misunderstood, so 
that a day was actually added every third instead of every 
fourth year, until the year 9 B.C. inclusive. To correct 
this error, the Emperor Augustus directed that no further 
intercalation should be made till the sixteenth year follow- 
ing, which was the year 8 A.D. In honor of this correction 
an obsequious senate changed the name of the month Sex- 
tilis to Augustus, and in order that this month should be of 
the same length as the month Julius it was increased by one 
day taken from Februarius ; then, to prevent 3 long months 
from coming in succession, one day was transferred from 
September to October and one day from November to De- 
cember. These changes having been made, the order of the 
months and their lengths was the same as we 6nd them now, 
and the calendar, thus perfected, remained without further 
alteration for nearly 16 centuries. o 

According to the Roman method of counting the days of 
the month -backward from the first day of the succeeding 
month, it happened that the 23d of February in every com- 
mon year was called sexto calendas Martias ; the intercalated 
day in the fourth year of each quadrennium was called bis 
sexto calendas Martias; hence, the fourth year of the 
quadrennium came to be called a bissextile year. 

A common year contains one day more than 52 weeks ; 
consequently the years that follow common years begin one 
day later in the week. The years that follow bissextile 
years begin two days later in the week, that is, they skip or 



Of calendars. 215 

leap over one day ; hence, bissextile years are frequently 
called leap years. 

The Gregorian Reformation. 

168. The average Julian year being .0078 of a day 
longer than the tropical year, the Julian date of the ver- 
nal equinox must fall back by that amount annually, in the 
same way that a clock which runs too slow falls behind one 
that keeps accurate time. At the time of the Julian Refor- 
mation, the date of the vernal equinox was March 24th, but 
at the time of the Council of Nice, 325 A. D., it had 
fallen back to March 21st. Now it was this council that 
fixed the time of Easter by declaring that it should be 
celebrated on the first Sunday following the full moon that 
happened on, or next after, the vernal equinox. 

At the time of Pope Gregory XIII., the date of the ver- 
nal equinox had fallen back to March 11th, and a corres- 
ponding change had taken place in the date of Easter. To 
remedy this defect in the calendar, Gregory proposed a 
change which was adopted by the ecclesiastical council that 
assembled in 1582. To restore the date of the equinox to 
what it was in the year 325, ten days were added to the Julian 
count, and to prevent a recurrence of the difficulty, it was 
agreed to omit the intercalary day in each subsequent cen- 
tesimal year, whose number is not divisible by 400. Accord- 
ing to this scheme the rule for determining the length of a 
year may be written as follows : every year ivhose number 
is not divisible by 4 and every centesimal year ivhose number 
is not divisible by JfiO is a common year of 365 days ; all 
other years are leap years of 866 days. 

The calendar thus revised was adopted at once in the 
principal Catholic countries, but more slowly in other 
countries. It w r as not adopted in Great Britain till 1752, 
at which time, because of the omission of the intercalary 
day in 1700, the difference between the Julian and the 



216 ASTRONOMY. 

Gregorian count had become 11 days. At the same time 
the beginning of the year was changed from the 25th of 
March to the 1st of January. Parliament enacted that the 
year 1752, which began on the 25th of March, should end 
on the 31st of December, and also that the day following 
September 2, 1752, should be called the 14th of September. 

These changes gave rise to two methods of writing dates : 
the old style (0. S.) and the new style (N. S.), the 
former being the Julian and the latter the Gregorian 
date. 

As an illustration of the effect of the change of style, we 
may instance the case of Washington. He was born Febru- 
ary 11, 1732, before the change of style. Inasmuch as 1752 
began on the 25th of March and ended on the 31st of De- 
cember, he had no birth-day in that year ; hence, he was 20 
years old on the 22d of February, 1753, new style. Because 
anniversaries are always determined according to the civil 
calendar, the birth-day of Washington is properly cele- 
brated on the 22d of February, and not on the 23d, as some 
have contended, on account of the day dropped in the year 
1800. 

Notes on the Civil Calendar. 

169. The years as named in the civil calendar are years 
current. There is no such thing as a year. In order, 
therefore, that the years before and after the beginning of 
the Christian era may be reckoned in a continuous series, 
the numbers denoting years B. C. must be diminished by 1 : 
thus, the year 45 B. C. is the same as —44 A. D. 

From this principle it follows also that a century does not 
end till the end of the centesimal year. Thus, the 18th 
century did not end till December 31, 1800. 

The difference between the old and new style is now 
equal to 12 days, in consequence of the omission of an 
intercalary day in the year 1800. This is the difference 



OF CALENDARS. 217 

between our own dates and those of Kussia, which still 
adheres to the Julian calendar. 

With the corrections already noted, the civil calendar will 
not depart from the astronomical reckoning by so much as 
one day before the year 5,000 A. D. 

The Ecclesiastical Calendar. 

170. The ecclesiastical calendar as it now exists was 
formed by bringing a system of artificial periods, called 
calendar lunar months, into harmony with the Gregorian 
Calendar. Its most important use is the determination of 
the dates of the movable fasts and festivals of the church. 
This determination depends, so far as we are concerned, 
upon the English law, which says, " . ... Easter Day, on 
which the rest depend, is always the first Sunday after the 
full moon that happens upon or next after the 21st day of 

March " The full moon referred to has always been 

understood to mean the 14th day of the calendar lunar 
month. 

The Lunar Cycle, Golden Number, and Epact. 

171. The lunar cycle is a period of 19 Gregorian years, 
which coincides very closely with 235 mean lunar months. 
It begins with the year in which the new moon of the calen- 
dar lunar month falls on the 1st of January, and the num- 
ber of any year of the cycle is called the golden number 
of that year. The present cycle commenced with 1881, so 
that the golden number of 1883 is 3, that of 1884 is 4, and 
so on. 

A lunar cycle is divided into calendar lunar months as 
follows : the first month of any year is a solid month of 
30 days; the second is a hollow month of 29 days, unless 
it includes the 29th of February, in which case it is a solid 
month; the third is solid ; the fourth is hollow, and so on 
alternately to the end of the year. The residual days at the 



218 ASTKONOMY. 

end of each calendar year are carried forward to form a part 
of the first month of the following year, until by accumula- 
tion they amount to 30 or more, in which case an embolis- 
mic month of 30 days is formed, and the remaining days 
are carried forward as before, and so on to the end of the 
cycle, which closes with a hollow month of 29 days. 

The number of days carried forward to any year is the 
epact of that year. Hence, the epact of a year is the age 
of the calendar moon at the end of the preceding year. The 
epact for 1881, the first year of the present cycle, is 0; for 
1882 it is 11 ; for 1883 it is 22 ; for 1884 it is 33 — 30, or 3, 
and so on to the last year of the cycle, for which it is 18. 
From what precedes, it is evident that the epact for any 
year may be found by the following 

RULE. 

Diminish its golden number by 1 ; multiply the 
remainder by 11; and divide the product by SO; 
the remainder will be the epact required. 

Because the epact is also the age of the calendar moon at 
the end of February, we can easily deduce the time of the 
full moon that precedes Easter. Thus, for 1883 the epact 
is 22 ; subtracting this from 30, we have the day that the 
March moon ends ; increasing the remainder, which is 8, 
by 14, we have the time of the following full moon, which 
is March 22d. 

Correction of the Epact. 

172. When long periods of time are taken into account 
it is found that the average length of the calendar lunar 
month is a little less than that of a mean lunar month. 
This difference amounts by accumulation to 1 day in about 
300 years. To take account of this error and to bring the 
calendar moon into harmony with the actual moon of the 



OF CALENDARS. 219 

heavens, it has been agreed to augment the length of one of 
the calendar lunar months by 1 day in every period of 300 
years. This is done by diminishing the epact by 1 at every 
300th year. This correction was made in 1800, and will be 
repeated in the years 2100, 2400, etc. 

The Dominical Letter and the Solar Cycle. 

173. The days of the year were formerly designated by 
letters, A being written opposite the first, B opposite the 
second, and so on to G-, which stood opposite the seventh 
day, after which the same letters and in the same order 
were continually repeated to the end of the ,year, always 
skipping over the 29th of February. The letter opposite 
Sunday in any year was called the Dominical or Sunday- 
letter of that year. In common years there is but one 
Sunday letter, but in leap years there are two, one before 
the 29th of February and the other after ; as the latter is 
most used in practice, it is taken for the Dominical letter 
of the year, the former being neglected. 

It is easily seen that the Sunday letter falls back one place 
every common year and two places every leap year ; thus, the 
Dominical letter for 1881 is B; for 1882 it is A ; for 1883 it 
is G ; and for 1884 it is E. 

In a regular quadriennium of 4 Julian years the Sunday 
letter falls back 5 places, and in 7 such periods it falls back 
35 places, or 5 entire cycles, after which the days of the 
week recur on the same days of the year as in the preceding 
cycle. This period of 28 years is called the solar cycle. 

The preceding principles enable us to compute the num- 
ber of the Dominical letter for any year, but for practical 
purposes it is found more convenient to use Table I., from 
which we can take out the Sunday letter for any year from 
1600 A.D. up to 2400 A.D. 

A simple inspection of the table is sufficient to suggest the 
method of its formation. 



220 



ASTRONOMY. 



TABLE I 











Centuries. 










Years in Excess 












Years in Excess 










of Centuries. 




2000 


2100 


2200 


2300 




of Centuries. 








1600 


1700 


1800 


1900 













23 


34 


45 


A 


C 


E 


G 


56 




79 


90 


1 


12 




35 


46 


Q 


B 


D 


F 


57 


68 




91 


2 


13 


24 




47 


F 


A 


C 


E 


58 


69 


80 




3 


14 


25 


36 




E 


G 


B 


D 


59 


70 


81 


92 




15 


26 


37 


48 


1) 


F 


A 


C 




71 


82 


93 


'I 




27 


38 


49 


C 


E 


G 


B 


60 




83 


94 


5 


16 




39 


50 


B 


D 


F 


A 


61 


72 




95 


6 


17 


28 




51 


A 


C 


E 


G 


62 


73 


84 




7 


18 


29 


40 




G 


B 


D 


F 


63 


74 


85 


96 




19 


30 


41 


52 


F 


A 


c 


E 




75 


86 


-97 


*8 




31 


42 


53 


E 


G 


B 


D 


64 




87 


98 


9 


20 




43 


54 


D 


F 


A 


C 


65 


76 




99 


10 


21 


32 




55 


C 


E 


G 


B 


66 


77 


88 




11 


22 


33 


44 




B 


D 


F 


A 


67 


78 


89 





Explanation. The table indicates the Dominical letter for every Gregoriau 
year from 1600 A.D. up to 2400. To use it, we find the exact century of the year at 
the top of one of the four middle columns, and the excess over exact centuries in 
one of the columns on the right or left ; the required Dominical letter will be found 
in the same column as the former and in the same line as the latter. 



Examples. Let it be required to find the Dominical let- 
ters for the years 1799, 1800, and 1804. In the column 
headed 1700, and on the same line as 99, we find F ; hence, 
F is the Dominical letter for 1799 ; in like manner we find 
that the Dominical letter for 1800 is E, and that for 1804 
is G. The year 1804 being a leap year, the Dominical let- 
ter given in the table is the one that follows February 29th ; 
for the time preceding that date the Dominical letter is A. 

When we know the Sunday letter for any year, we can 
easily find the day of the week corresponding to the 1st of 
January, from which we can, by a simple computation, find 
the day of the week corresponding to any day of the year. 
This operation is more conveniently performed by means 



OF CALENDARS. 



221 



of Table II., from which we can at once take out the day 
of the week corresponding to the 1st, 8th, 15th, 22d, and 
29th days of any month. 



TABLE II 



Common Years. 


Dominical Letters. 


Leap Years. 


A 


B C D E 


F 


G 


Jan., Oct 

May 


S 

Mon. 

Tu. 

Wed. 

Th. 

Fr. 

Sat. 


Sat. |Fr. Th. 
S. Sat. Fr. 
Mon. S. Sat.. 


Wed. 

Th. 

Fr. 

Sat. 
S. 


Tu. 

Wed. 

Th. 

Fr. 

Sat. 


Mon. 

Tu. 

Wed 

Th. 

Fr. 

Sat. 

S. 


October. 

May. 

Feb , Aug. 

Mar., Nov. 

June. 

Sept., Dec. 

Jan., Apr., July. 


Feb., Mar., Nov. 


Tu. 
Wed. 
Th. 
Fr. 


Mon.. S. 
Tu. Mon. 
Wed. Tu. 
Th. Wed. 


Sept., Dec 

April, July 


Mon. 
Tu. 


S. 
Mon. 



Explanation. To use Table II., find the month in the left-hand 
column for common years, and in the right-hand column for leap 
years ; then in the same line and under the Dominical letter for the 
year will be found the day of the Aveek corresponding to the 1st, 8th, 
15th, 22d, aud 29th days of that month. 

Examples. 1°. The battle of Bunker Hill was fought 
June 17th, 1775 : on what day of the week did it occur? 

Solution. From Table I. we see that the Dominical 
letter for 1775 was A ; from Table II., under the letter A 
and opposite June, we find Th. ; hence, the 15th of June 
was Thursday, and consequently the 17th was Saturday. 

2°. On what day of the month was Easter in the year 
1883? 

Solution". We have already seen that the calendar full 
moon of March fell on the 22d. By means of Tables I. and 
II. we find that the 22d of March fell on Thursday ; hence, 
the following Sunday, which was Easter, came on the 25th. 



Chronological Cycles. 

174. Besides the solar cycle of 28 years and the lunar 
cycle of 19 years, both of which are astronomical, the Ro- 



222 ASTRONOMY. 

mans made use of a civil cycle of 15 years called the Cycle 
of Indiction. This cycle was used in the courts of law, 
and in the fiscal administration of the empire, and its use 
was thus introduced into legal dates. 

Different nations have reckoned time from different 
epochs, and sometimes in different units; but for the con- 
venience of astronomers and chronologists it has been 
found desirable to have a common epoch from which time 
is to be reckoned in terms of the same unit. For this 
reason it has been agreed to form a grand cycle of 7,980 
Julian years based upon the three cycles already mentioned. 

This cycle, which is called the Julian Period, com- 
mences with the beginning of the year 4713 B. C, which 
epoch is also the beginning of a solar cycle, of a lunar cycle, 
and of a Cycle of Indiction. Because 7980 is the least 
common multiple of 28, 19, and 15, it is obvious that the 
first years of all three of these cycles cannot again concur till 
the beginning of the year 3268 A. D., which will be the first 
year of the next Julian Period. To find the year of the 
Julian Period corresponding to any calendar year, we have 
only to add the number of the calendar year to 4713 : thus, 
the calendar year 1884 A. D. is the 6597th year of the 
Julian Period. When this style of reckoning is used for 
determining specific dates, these dates must first be reduced 
to the Julian, or old style. 

If we know the year of the Julian Period, it is obvious 
that we can find the corresponding years of the subordinate 
cycles by the following simple rules : 

T. To find the y ear of the solar cycle : divide the 
year of the Julian Period by 28 ; if the remainder 
is not it will denote the year of the solar cycle, or 
if it is the given year will be the 28th year of the 
solar cycle. 

2°. To find the year of the lunar cycle : divide the 
year of the Julian Period by 19 ; if the remainder 



Of calendars. 223 

is not it will denote the year of the lunar cycle, or 
if it is 0, the given year will be the 19th year of the 
lunar cycle. 

3°. To find the year of the cycle of indiction : di- 
vide the year of the Julian Period by 15; if the 
remainder is not it will denote the year of the 
indiction cycle, or if it is 0, the given year ivill 
be the 15th of the cycle of indiction. 

The year 1884 A.D. is the 6597th year of the Julian 
Period. Dividing 6597 in succession by 28, 19, and 15, we 
find the respective remainders 17, 4, and 12 ; hence, 1884 
is the 17th year of the solar cycle, the 4th year of the lunar 
cycle, and the 12th year of the cycle of indiction; these 
numbers are generally given in the almanacs. 

It is to be observed that the lunar cycle above referred 
to, is supposed to be exactly equal to 19 Julian years; it is 
therefore an artificial cycle. Hence, the above rale for find- 
ing the year of the lunar cycle will require a correction for 
ecclesiastical purposes as explained in Art. 172. 

The Dionysian Period is a period formed by a com- 
bination of the lunar and the solar cycles ; its length is 
equal to 28 x 19, or 532 years. This period marks the 
recurrence of new moon on the same day of the week and 
the same day of the month throughout the year. It is 
used by chronologists in verifying dates. 

To find the year of the Dionysian Period corres- 
ponding to any calendar year, ive first find the year 
of the Julian Period, and then divide its number 
by 582 ; the remainder, if not 0, will denote the 
year of the Dionysian Period, or if the remainder is 
the year is the 53%d of the Dionysian Period. 

Thus, 1884 is the 6597th year of the Julian Period: 
dividing 6597 by 532 we find a remainder equal to 213, 



224 ASTRONOMY. 

Hence, the . year 1884 is the 213th year of the current 
Dionysian Period. In the example just given the quotient 
found was 12 ; hence, 12 entire periods have elapsed, and 
we are now in the 13th Dionysian Cycle of the current 
Julian Period. 

By applying the preceding rules we find that the first 
year of the Christian era was the 10th year of the 169th 
solar cycle, the 2d year of the 249th lunar cycle, the 4th year 
of the 315th indiction cycle, and the 458th year of the 9th 
Dionysian cycle of the current Julian Period. 



X. PLANETS AND SATELLITES. 

Preliminary. 

175. The general relations of the planets with respect to 
each other and with respect to the sun have been explained 
in preceding parts of this work. It is now proposed to 
point out some of their individual peculiarities and also to 
give an account of their satellites and other appendages. 
This branch of the subject will treat more particularly of 
the forms and magnitudes of the planets, of their times of 
rotation, of their telescopic appearances, and of their physi- 
cal conditions ; it will also contain an explanation of their 
satellite systems, and of the ring system of Saturn. The 
data employed will be those laid down in Tables I., II. , III., 
Arts. 46, 47, and 51, which are only approximate ; it is 
therefore to be borne in mind that they are subject to cor- 
rection for reasons similar to that given in the note to 
Table I. 

MERCURY. % . 

Magnitude, Distance, and Periodic Time. 

176. Mercury is the smallest of the eight principal 
planets, and is also the nearest to the sun. Its diameter 
is 2,990 miles, which is but little more than f of the earth's 
mean diameter ; his surface is therefore about \ of the 
earth's surface, and his volume about -^ of the earth's 
volume. 

Mercury revolves around the sun in a little less than 88 
days, its mean distance from that body being about 35f 
millions of miles. In consequence of the great excentricity 



226 ASTRONOMY, 

of his orbit, he alternately approaches the sun to within 28 J 
millions of miles, and recedes from it to a distance of 43 
millions of miles. 

Synodic Period, Elongation, and Visibility. 

177. His synodic period, counted from inferior conjunc- 
tion to inferior conjunction, is a trifle less than 116 days. 
At the beginning of this period he is at the middle of his 
arc of retrogradation, which on an average amounts to 
about 12^°. The time occupied in passing over this arc 
is about 22 days; during the remainder of the period 
his motion is direct ; hence, the planet advances for about 
94 days, and then retrogrades for about 22 days, and so 
on alternately. Once during each synodic period he is 
at his greatest eastern and once at his greatest western 
elongation. 

In consequence of the planet's proximity to the sun, he 
is only visible to the naked eye for a few days at the time 
of his greatest elongation ; it is seen after sunset at the time 
of eastern and before sunrise at the time of western elonga- 
tion ; these times will be more or less favorable for observa- 
tion, according to the amount of the elongation and the 
obliquity of the planet's orbit to the horizon. 

Inasmuch as the inclination of the planet's orbit to the 
ecliptic is only about 7°, its inclination to the western hori- 
zon at sunset will be greatest in the spring of the year, and 
its inclination to the eastern horizon at sunrise will be 
greatest in the fall of the year. The greatest elongation 
will have different values at different times, being dependent 
on the distances both of the earth and of Mercury from the 
sun, as may be seen from Fig. 88 ; it may have any value 
from 17f° to 28°. The former value corresponds to the 
least distance of Mercury and the greatest distance of the 
earth from the sun, and the latter to the greatest distance 
of Mercury and the least distance of the earth from the 
sun. 



PLANETS AND SATELLITES. 227 

Explanation. ACM represents the M 

orbit of Mercury, S the sun, E the earth, *r7^\ "~"\ 

and M the place of Mercury when the .^-'~~'/ \ \ 

line EM is tangent to the orbit. SEM is | ..--"'' \ e I \ \ 

then the greatest elongation, and if we El""" ""* \ ~Q fC 

suppose SM to be perpendicular to EM, yf A\ / 

we shall have • \. S 

SM ^^ "~ -~ ^ 

Sm = SE" Fig. 88. Elongation of Mercury. 

Making SM equal to 281 millions of miles 

and SE equal to 94 millions of miles, we find the least value of SEM equal to 17° 
40' ; making SM equal to 43 millions of miles and SE equal to 91 millions of miles, 
we find SEM equal to 28" 12'. 

When Mercury is visible to the naked eye it shines with 
a clear white light, appearing like a bright star of the first 
magnitude. Under favorable circumstances it is often visi- 
ble in the latitude of New York for 6 or 8 days both before 
and after its greatest elongation. 

Phases and Telescopic Appearance. 

178. When viewed with a suitable telescope, Mercury is 
found to have phases like the moon, and which are ac- 
counted for in the same manner. The cycle of his phases 
is a synodic period ; at the time of inferior conjunction his 
illuminated face is turned from the earth, and the planet is 
invisible unless it happens to pass exactly between the earth 
and the sun ; when he emerges from the glare of the sun's 
rays so as to be seen with a telescope his phase is crescent ; 
as he advances toward elongation the thickness of the cres- 
cent increases, and at his greatest elongation he has the 
same phase as the moon at first quarter ; from this time to 
superior conjunction his phase is gibbous ; at superior con- 
junction his illuminated hemisphere is turned directly 
toward us, but the planet is invisible, being enveloped and 
overpowered by the sun's rays. From superior conjunction 
back to inferior conjunction these phases are repeated, but 
in reverse order. 

The telescope reveals no markings from which his time 
of rotation on an axis can be inferred with certainty, though 



228 ASTRONOMY. 

Schroter assigned a rotation period of 24h. 5m. The ap- 
pearances on which this astronomer based his conclusion 
are now regarded as fallacious. The fact that the planet 
shows no markings has led some to suppose that he is sur- 
rounded by a dense mass of clouds or vapors. Observations 
at the times of transit indicate a pretty dense atmosphere. 

Transits of Mercury. 

179. The earth in his annual path crosses the line of 
nodes of the orbit of Mercury about the 7th of May and the 
9th of November; if the planet happens to be at inferior 
conjunction within 2 or 3 days of either of these dates, he 
will probably be so near the ecliptic that he will pass directly 
between the earth and the sun, in which case he will be seen 
like a round black spot, moving from east to west across the 
solar disk ; this phenomenon is called a transit of Mer- 
cury. 

A cycle of 46 sidereal years differs from 191 sidereal 
periods of Mercury by less than one-third of a day ; hence, 
if there is a transit very near either node at any time, cor- 
responding transits will recur at that node every 46 years, 
for a pretty long period. During the 46-year cycle there 
are usually 6 transits, 4 of which at present occur at the 
ascending node in November, and 2 at the descending node 
in May. This cycle of transits is, like the eclipse cycle, 
only approximate ; as in case of the Saros, new transits enter 
the cycle from time to time and old ones pass out. 

The last transit of Mercury took place November 7, 1881; 
it was a recurrence of the transit of November 7, 1835. The 
next transit will be on May 9, 1891 ; this will be a recur- 
rence of the transits of May 6, 1799 and May 8, 1845 ; after 
1891 it will probably pass out of the cycle. The transit of 
November 10, 1894, will be a recurrence of the transits of 
November 9, 1802 and November 10, 1848. 

The transits of Mercury are valued by astronomers prin- 



PLANETS AND SATELLITES. 220 

cipally on account of the opportunity they afford for verify- 
ing and correcting the tables of that planet. It was from a 
comparison of observations made on these transits that 
Leverrier reached the conclusion that the perihelion of 
Mercury's orbit is moving more rapidly than can be ac- 
counted for by the perturbations of known planets, and 
which led him to suggest the existence of a group of small 
planets lying between Mercury and the sun. The actual 
existence of these intra-Mercurial bodies has not, as yet, 
been established. 

Venus. ? . 
Magnitude, Periodic Time, and Distance. 

180. Venus is the third of the principal planets in order 
of magnitude, counting from the smallest, and the second 
in order of distance from the sun. Her diameter is 7,660 
miles, which is only 4 per cent, less than that of the earth ; 
we may say therefore that her volume is very nearly equal 
to that of the earth. She completes a sidereal revolution 
around the sun in a little less than 225 days, her mean dis- 
tance from that body being 66f millions of miles. Her orbit 
is less excentric than that of any other principal planet, her 
least distance from the sun being about 6fi|- millions of 
miles, and her greatest distance 67J- millions of miles. 

Synodic Period, Elongation, and Visibility. 

181. The synodic period of Venus, counting from inferior 
conjunction to inferior conjunction, is nearly 584 days. At 
the beginning of this period she is at the middle of her arc 
of retrogradation, which is equal to nearly 16° ; the time 
occupied in traversing this arc is about 41 days ; during the 
remainder of the period her motion is direct; hence, the 
planet advances 543 days and retrogrades 41 days in a com- 
plete synodic revolution. Once during each synodic period 



230 ASTKONOMY. 

she is at her greatest eastern and once at her greatest west- 
ern elongation. 

Except for a few days at the times of her inferior and 
superior conjunction she is visible to the naked eye, half of 
the time on the east of the sun in the evening and half of 
the time on the west of the sun in the morning. In the 
former case it is called the evening star, and in the latter 
case the morning star; the ancients, thinking these to be 
different bodies, called the evening star Hesperus and 
the morning star Lucifer. 

When Venus is far enough from the sun to be seen after 
twilight in the evening, or before twilight in the morning, 
she shines with a brilliant white light. At her maximum 
brilliancy she is the brightest of all the planets; at these 
times she can often be seen with the naked eye at midday, 
and at night her light is intense enough to form shadows 
of dark objects on a light ground. Her greatest elongations 
are more nearly equal than those of Mercury; the maximum 
value of her greatest elongation, found in the manner al- 
ready described, is 47° 40', and its minimum value is 44° 
50', the average being a little over 46°. She has the great- 
est brilliancy when her elongation is about 40°, just before 
reaching her greatest western, or just after passing her 
greatest eastern elongation ; she reaches the former point 
about 2 months after, and the latter point about 2 months 
before she is at inferior conjunction. 

Phases, and Distances from the Earth. 

182. Venus passes through the same succession of phases 
as Mercury. In moving from inferior conjunction to the 
greatest western elongation her phase is crescent ; at the 
greatest elongation it becomes dichotomous ; after this it 
becomes gibbons, and it is only at superior conjunction that 
her illuminated face is turned fully toward the earth. In 
traveling back to inferior conjunction the same phases recur, 
but in reverse order. The cycle of her phases is a synodic 



PLANETS AXD SATELLITES. 231 

period, but the duration of the crescent is much shorter 
than that of the gibbous phase ; the time occupied in pass- 
ing from inferior conjunction to the greatest western elon- 
gation is no more than 71 days, while she occupies a period 
of 221 days in moving from this place to superior con- 
junction. 

The brilliancy of the planet depends upon her phase and 
also upon her distance from the earth, which varies very 
considerably. When at inferior conjunction her distance 
from the earth is only 25 or 26 millions of miles ; at her 
greatest elongation this distance is about 66 millions of 
miles ; and at superior conjunction it is nearly 160 millions 
of miles. As her apparent diameter varies inversely as her 
distance from the earth, it is more than 6 times as great 
when nearest the earth as it is when she is farthest removed. 
The relative sizes of her disk at different distances is shown 
in Fig. 89. 




Fig. 89. Phases of Venus. 

Explanation. Fig. 89 represents three different phases of Venus. The figure 
on the right represents her apparent size and her phase just before or just after 
inferior conjunction ; the figure on the left shows her apparent size and her 
phase at the time of her superior conjunction ; the middle figure shows her ap- 
parent size and her phase when she is between her greatest elongation and her 
superior conjunction. 

The combined effect of phase and distance gives the 
most brilliant surface, as was before stated, about 10 days 



232 ASTEOKOMY. 

before the planet reaches her greatest western and about 
the same time after she has passed her greatest eastern 
elongation. 

Atmosphere. Telescopic Appearance. 

183. Venus is undoubtedly surrounded by a dense at- 
mosphere. Schroter noticed that the narrow crescent which 
the planet presented near the time of inferior conjunction 
extended considerably beyond its natural limit of 180°, a 
phenomenon which has since been witnessed by many other 
observers. At the time of inferior conjunction in 1866, 
Prof. Lyman, of Yale College, watched the planet from 
day to day until its nearest limb was only 1° 8' from the 
sun. The slender crescent became more and more extended 
beyond 180°, until at favorable moments it was seen as a 
complete ring of light surrounding the dark body of the 
planet. This prolongation of the cusps can only be ex- 
plained by supposing the solar rays to be refracted in pass- 
ing through the atmosphere of Venus ; the observations of 
Prof. Lyman indicate that the refraction of a horizontal ray 
is about 45'. From observations made at Dorpat in 1849, 
Madler concluded that the refraction of a horizontal ray was 
nearly 44', which is about one-third greater than that pro- 
duced by the earth's atmosphere. Observations made upon 
Venus while in transit across the sun's disk are equally 
indicative of an atmosphere. 

Prof. Newcomb, in giving an account of his observation 
on the last transit, before the Eoyal Astronomical Society, 
says : " There was but one physical phenomenon that was 
worthy of note, and that was so well marked that it could 
not escape any one ; it was a line of light that surrounded 
the dark hemisphere of Venus which was off the sun. I 
looked very carefully before first contact to see whether it 
was possible to see Venus projected upon the corona, but 
was unable to see any sign of the planet until it had actu- 
ally entered upon the sun's disk. When it was half way on, 



PLANETS AND SATELLITES. 233 

it appeared as if a piece of the sun had been sharply cut out 
with a knife ; and the line of light which has been described 
by so' many observers, and which I had looked for in vain 
before, began to show itself ; but it was not continuous all 
around the planet ; on the contrary, it was only seen at 
certain points. As the internal contact approached, I found 
that the line of light slowly became brighter, and for some 
seconds before internal contact it was quite continuous, and 
was seen as a fine arc of light joining the cusps of the sun." 

Similar appearances were observed by many other astron- 
omers who watched the transit. It has been suggested that 
the atmosphere is at places loaded with clouds. Mr. Hug- 
gins several years ago found certain lines in the spectrum 
of Venus, which are attributable to watery vapor in her 
atmosphere; Prof. Young says that the same thing was 
very clearly indicated during the recent transit. 

When viewed with a telescope its light is so dazzling as 
to suggest the idea that the body of the planet is sur- 
rounded by white clouds, which reflect light far better than 
ordinary land and water. It is possible that this layer of 
clouds covers up and obscures the surface markings which 
some observers are said to have seen. It is probable, though 
not certain, that the planet revolves on an axis ; Schroter 
assigned a period of 23J hours, but this determination is 
not universally accepted. 

Transits of Venus. 

184. The earth, in her annual revolution, crosses the 
line of nodes of the orbit of Venus about the 5th of June 
and the 7th of December ; and when it happens, as it does 
at long intervals, that Venus is in inferior conjunction at 
either of these times, the planet will pass directly between 
the earth and the sun ; this phenomenon is called a tran- 
sit of Venus. 

Because 243 sidereal years correspond to 395 sidereal 



234 ASTRONOMY 

periods of Venus within less than one -third of a day, it fol- 
lows that a transit of Venus, which takes place very near 
either node, will recur at intervals of 243 years, and this 
for a long period. During this cycle of 243 years there are 
usually four transits, of which two happen at the ascending 
node in June, and two at the descending node in Decem- 
ber. The two that occur at either node are separated by 
an interval of 8 years; from the last transit at one node to 
the first at the other is alternately 121^ and 105-|- years. 

The transit which took place on the 8th of December, 
1874, was a recurrence of the transit of December 7, 1631 ; 
and that of December 6, 1882, was a recurrence of the tran- 
sit of December 4, 1639. The transit of June 5, 1761, 
will recur on the 8th of June, 2004, and that of June 3, 
1769, will recur on the 6th of June, 2012. These two 
transits will be the next that will happen till the year 2117. 
As already explained, the transits of Venus are utilized by 
astronomers to determine the solar parallax. The transit 
of 1874 was extensively observed, as was also that of 1882. 
The results of the numerous observations made in those 
years have not yet been fully discussed. 

Comparison of Mercury and Venus. 

185. The planets Mercury and Venus resemble each 
other in many respects. The apparent motions of both are 
very similar ; both move back and forth with a shuttle-like 
motion in regard to the sun, which body they seem to fol- 
low in its general motion around the celestial sphere. 
Neither of them presents any decided marking, but the 
periods of rotation assigned to them by Schroter are very 
nearly equal. Both are supposed to be surrounded by layers 
of clouds floating in dense atmospheres. They resemble 
each other in their phases, in their arcs of retrogradation, 
and in their transits. Finally, they are the only planets 
that have no satellites. 



placets ahd satellites. 235 

Maes. $ . 
Magnitude, Periodic Time, and Distance. 

186. Mars, the fourth of the principal planets in order 
of distance from the sun, is next to the smallest in order of 
magnitude, Mercury alone being smaller. Like the earth, 
its form is that of an oblate spheroid ; its equatorial diameter 
is 4,220 miles, its polar diameter is 4,196 miles, and its 
mean diameter is 4,212 miles, the term mean diameter being 
used to denote the diameter of an equivalent sphere. 
Hence, its surface is considerably less than J of the earth's 
surface, and its volume is not far from \ of the earth's 
volume. 

He revolves around the sun in about 687 days, his mean 
distance from that body being 141 millions of miles. In 
consequence of the great excentricity of his orbit, he may 
approach to within 128 millions of miles of that body, and 
he may recede from it to a distance of 154 millions of miles. 

When in opposition his average distance from the earth 
is about 48 millions of miles; but if opposition happens 
when the planet is near perihelion, this distance may be- 
come as small as 35 millions of miles ; or if it occurs when 
the planet is near aphelion, this distance may become as 
great as 62 millions of miles. 

The mean distance of the planet from the earth at the 
time of conjunction is about 233 millions of miles, but this 
distance may be as small as 220 and as great as 246 millions 
of miles. Hence, the extreme range of the planet's distance 
from the earth is from 35 to 246 millions of miles. This 
change of distance makes the variation of his apparent 
diameter very great, and consequently produces a corres- 
ponding variation in the brightness of the planet. When 
nearest the earth, the apparent diameter of the planet is 
more than 7 times as great* as when it is farthest from the 
earth. 



236 ASTRONOMY. 



Synodic Period — Varying Brilliancy. 

187. The average value of the synodic period of Mars, 
counting from opposition to opposition, is a trifle less than 
780 days or nearly 26 months. Being a superior planet, it 
is at the middle of its arc of retrogradation at the time of 
opposition. The average value of this arc is about 15°, and 
the time required for the planet to move over it is about 70 
days ; hence, during each synodic period the planet retro- 
grades for 70 days, and its motion is direct for 710 days. 
The values above given are average values, and in conse- 
quence of the relative positions and shapes of the orbits of 
Mars and the earth, they will experience considerable varia- 
tion at different periods. 

The brilliancy of the planet is greatest when nearest to 
the earth, and least when farthest from the earth. When 
in opposition he is always more brilliant than any star of 
the first magnitude, and under favorable circumstances he 
is nearly as bright as Jupiter. When near conjunction his 
brilliancy diminishes to that of a star of the second magni- 
tude. In all cases his light is of a decided red color, but 
his ruddy hue is most conspicuous Avhen he is brightest. 

The earth crosses the line from the sun to the perihelion 
point of the orbit of Mars on the 27th of August in each 
year ; if the planet is in opposition at this time he will be 
at his least possible distance from the earth, and conse- 
quently in the most favorable position for observation. Of 
course this state of affairs can only occur at immensely long 
intervals ; but it frequently happens that opposition takes 
place within a few days of the 27th of August, and opposi- 
tions of this kind are utilized by astronomers for determin- 
ing the solar parallax, and for studying the physical char- 
acter of the planet. The opposition of 1877 took place 
about 9 days after Mars had passed his perihelion, and was 
regarded as a remarkably favorable one by astronomers ; a 



PLACETS AXD SATELLITES. 23? 

similar opposition took place in 1862, and another will 
occur in 1892. 

Telescopic Appearances, Rotation, and Physical Condition. 

188. Under the telescope, Mars is seen to be covered with 
large and irregular patches of a dusky red color which are 
supposed to be islands and continents ; the remaining por- 
tions of his surface, which are of a faint greenish tiut, are 
supposed to be seas and oceans. The outlines of these 
divisions are of a permanent character, but they are some- 
times obscured for a time and then reappear, as if the planet 
were surrounded by an atmosphere more or less loaded with 
clouds. The existence of such an atmosphere is well es- 
tablished, and we learn from the spectroscope that it con- 
tains watery vapor, and probably clouds like our own. 

From observations made on the spots it has been shown 
that Mars revolves on an axis in a period of 24h. 37m. 
22.73s. The planet has then his poles and an equator ; his 
equator is inclined to the plane of its orbit in an angle of 
about 27° ; hence, the planet has seasons somewhat similar 
to our own, except in length. The martial day is, as we 
have seen, a little longer than the terrestrial day, but the 
inequalities of day and night are similar to those experi- 
enced at different places on our earth. 

The martial year contains 668§ martial days, equal to 
nearly 687 terrestrial days ; in consequence of the great ex- 
centricity of the planet's orbit, the lengths of his seasons 
are more unequal than on our earth, summer in the north- 
ern hemisphere being 372 martial days and winter only 297 
days in length ; this division of time refers to the periods 
that the sun is on the northern and on the southern side of 
the martial equator. 

The telescope reveals the existence of two white spots, 
one at each pole ; the northern spot is nearly concentric 
with the corresponding pole, but the southern one is 
excentrically situated with respect to its corresponding 



238 ASTRONOMY. 

pole. It has been supposed that these spots are due to 
masses of ice and snow, a supposition which seems to be 
confirmed by their alternate decrease and increase according 
as the corresponding pole is turned toward or away from 
the sun. 

It has been suggested by some observers that the objects 
described above as snow-spots are, at least in part, made up 
of clouds. Trouvelot, who has given a great deal of study 
to the subject, says "during the winter seasons of the 
southern hemisphere of Mars the polar spots are most of 
the time invisible, being covered over by white, opaque, 
cloud-like forms strongly reflecting light." In 1877 he 
" mistook for the polar spots a canopy of clouds which cov- 
ered at least one-fifth of the surface of the whole disk." He 
says, "I only became aware of my error when the opaque 
cloud, beginning to dissolve at the approach of the martial 
summer, allowed the real polar spot to be seen through its 
vapors, as through a mist at first, and afterward with great 
distinctness." 

The telescope shows that Mars has phases, but not like 
those of Mercury and Venus. At opposition and at con- 
junction his illuminated face is turned toward the earth ; 
at intermediate periods he exhibits a gibbous phase corre- 
sponding to that of the moon two or three days before or 
after full moon. 

The surface of Mars has been charted, but the charts are 
of little value except to the professional astronomer ; the 
ordinary observer sees the outlines of oceans and continents 
only in perspective, and in consequence of the distortions 
produced in their apparent forms by the motions of the 
planet, he finds it almost impossible to recognize them at 
different times. 

Comparison of the Earth and Mars. 

189. We have already pointed out some analogies be- 
tween Mercury and Venus, but the Earth and Mars are 



PLANETS AND SATELLITES. 239 

more strikingly alike. Both of these planets are surrounded 
by atmospheres containing clouds and watery vapor ; their 
surfaces are alike diversified with continents and oceans; 
both have seasons which are only dissimilar in regard 
to length ; both have days and nights of nearly equal 
lengths, and which have their corresponding inequalities ; 
both have regions of snow and ice around their poles, which 
alternately increase and decrease with the cycle of the sea- 
sons ; in a word, these two planets resemble each other more 
strongly than any other two in the system. 

Satellites of Mars. 

190. Mars has two satellites, both of which were discov- 
ered by Prof. Asaph Hall in August, 1877 ; the outer one 
was first seen on the 11th, and the inner one on the 17th 
of that month. Both are extremely minute bodies, proba- 
bly not more than 6 or 8 miles in diameter, and both are 
very close to the surface of the planet. The planes of their 
orbits are very nearly coincident with the plane of the 
planet's equator. 

The outer satellite, the one first discovered, and which 
has been named Deimos, revolves around Mars in about 
30h. 17m. ; the inner one, called Phobos, performs its re- 
volution in 7h. 39m. The distance of the former from the 
centre of the planet is 14,350 miles, and that of the latter is 
no more than 5,830 miles. 

The motions of the satellites as seen from Mars must pre- 
sent some curious phenomena; in explaining them it will be 
found convenient to use martial time, that is, to count time 
in martial days, each of which is equal to 1.025 times a ter- 
restrial day. We readily find the periodic time of Deimos 
to be 1.231 days, or 29.55 martial hours, and that of Phobos 
to be .311 days, or 7.46 martial liours. 

An observer on the equator of Mars is carried from west 
to east by the rotation of the planet at the rate of 360° in a 
day; but the outer satellite is carried eastward by its orbital 



240 



ASTRONOMY. 



revolution at the rate of only about 292^° in a day; hence, to 
the supposed observer on the planet this satellite appears to 
move westward at the rate of 67^° a day, at which rate it 
would appear to make the circuit of the heavens in about 5^ 
days. Deimos therefore appears to an observer on Mars to 
rise in the east and to set in the west, the interval between 
two consecutive culminations over the meridian being 5J 
days. 

Phobos moves eastward in its orbit at the rate of more 
than 1154° per day, thus gaining on the supposed observer at 
the rate of more than 794° per day; as a consequence, this 
satellite rises in the west and sets in the east, the interval 
between two successive transits over the same meridian 
being only .45 of a day, or 10.8 martial hours. 

In consequence of the enormous horizontal parallaxes of 
the satellites, their diurnal circles are very unequally divided 
by the horizon ; the upper arc in case of Deimos being 160°, 
and in case of Phobos less than 138°. 



Explanation. The figure 
shows the equatorial section of 
Mars seen from the north side, 
and the orbits of the satellites 
supposed to be in the same plane. 
EW is the horizon of the ob- 
server, E being the east point and 
W the west jpoint. The angle 
OEM is nearly 8|°, and OCM is 
nearly 21^° ; hence, the upper 
arc EBW is equal to 163°, and 
the arc CAD to 137|°. Deimos 
*"* ''" rises at E and sets at W, remain- 

Showing the Apparent Motions ™g above the horizon 2.413d., or 
of the Satellites of Mars. 57h. 52m. ; Phobos rises at C and 

sets at D, being above the horizon 
about 4h. 10m. Deimos remains below the horizon for 69 hours, and 
Phobos for 6h. 40m. 

As the synodic periods of the satellites differ but little from their 




Fig. 90. 



PLANETS AND SATELLITES. 241 

sidereal periods, Deimos will go through its entire cycle of phases in 
about 30 hours, and Phobos in less than 8 hours. 

The fact that Phobos revolves from west to east at a more rapid 
rate than the planet itself, would seem to be an argument against the 
nebular hypothesis as it is usually enunciated. That hypothesis 
requires that a body shall move more slowly as its distance from the 
centre of motion becomes greater. 



The Planetoids. CD- 
General Description. 

191. Proceeding outward from the sun, we next meet 
with a group of small planets called Planetoids, or some- 
times Asteroids. The first of the group was discovered 
on the first day of the present century, namely on January 
1, 1801, by Piazzi, a noted Italian astronomer ; a second one 
was discovered in 1802, a third in 1804, and a fourth in 
1807, after which no additional ones were found till 1845. 
Since that time new members have been rapidly added to 
the group, sometimes as many as 8 or 10 in a single year, 
until now (1883) their number amounts to more than 230. 

The first four were named in the order of their discovery 
Ceres, Pallas, Juno, and Vesta ; the remaining ones have 
also received proper names, but the difficulty of remember- 
ing them has led to the practice of numbering them, the 
numbers denoting the order of discovery; thus, the 226th 
planetoid discovered is denoted by the symbol @. 

Nearly all of the planetoids are telescopic, although Ceres 
and Vesta can be seen with the naked eye under favorable 
circumstances ; in point of brilliancy they run from the 7th 
down to the 10th and 11th magnitudes, and some are even 
fainter; their actual magnitudes have not been determined, 
though we know that they are very small ; some of the 
larger ones are thought to be from 300 to 400 miles in 
diameter, while some of the smaller ones are supposed to be 
no more than 30 or 40 miles in diameter. 
11 



242 ASTRONOMY. 

Their orbits, which are elliptical, have a wide range, both 
in regard to excentricity and in their inclinations to the 
plane of the ecliptic ; thus, the excentricity of @, discov- 
ered by Watson, is .38, while that of is no more than 
.03 ; the inclination of the orbit of 0, or Pallas, is 35°, 
while that of ©, as well as that of several others, is less 
than 1°. Their mean distances from the sun vary from 
212 to 312 millions of miles, and their corresponding 
periods of revolution vary from 1195 to 2267 days. 

Some of the planetoids approach so near the earth at 
favorable oppositions that they are observed, like Mars, for 
the purpose of determining the solar parallax. Though at 
a greater distance from the earth, they present the advan- 
tage of appearing as shining points of moderate brilliancy, 
instead of showing dazzling disks like that of Mars. Ob- 
servations were made upon Flora, ©, in 1874, in both 
hemispheres, from which the value 8". 875 was deduced for 
the solar parallax. At the time of making these observa- 
tions the distance of the planet from the earth was about 
80 millions of miles. Some of the other planetoids are 
nearer to the earth than this at the time of favorable oppo- 
sition; thus, 0, when nearest the earth, is less than 60 
millions of miles distant. 



Jupiter. 2£. 

Magnitude and Form. 

192. Jupiter, the fifth principal planet in order of dis- 
tance from the sun, has been called the giant planet of the 
system ; it is greater, both in volume and in mass, than the 
aggregate of all the other planets together. 

Its form is that of an oblate spheroid, considerably com- 
pressed at the poles ; its equatorial diameter is 87,770 miles, 
and its polar diameter is 82,570 miles; its mean diameter is 
therefore equal to nearly 86,000 miles, which is about -^ of 



PLANETS AND SATELLITES. 243 

the diameter of the sun, and nearly 11 times that of the 
earth. His bulk is equal to more than 1280 such worlds as 
ours ; his density, however, is so much less than that of the 
earth that his mass is only 312 times as great. He is al- 
ways a conspicuous body in the heavens, and though he is 
occasionally less bright than Venus, he is on the average 
the most brilliant of all the planets. 

Periodic Time, and Synodic Period. 

193. Jupiter revolves around the sun in about 11.86 of 
our years; his synodic period is therefore a little less than 
399 days. During this period his motion is retrograde for 
about 120 days, and direct for about 279 days. His arc of 
retrogradation is a little less than 10°, the planet being at 
the middle of this arc when he is in opposition. 

Distance from the Sun and from the Earth. 

194. The mean distance of Jupiter from the sun is 480 
millions of miles, but on account of the excentricity of his 
orbit he may approach to within 457 millions of miles of 
that body, and may recede from it to a distance of 503 mil- 
lions of miles. 

His distance from the earth is a minimum at opposition 
and at a maximum at conjunction. These distances vary 
from one opposition to another and from one conjunction 
to another, being dependent upon the positions of both 
planets in their respective orbits. The least minimum dis- 
tance is 363 millions of miles, and the greatest minimum 
distance is 412 millions of miles ; the maximum distances 
vary from 542 to 597 millions of miles. The entire range 
in the planet's distance from the earth is from 363 to 597 
millions of miles, a range which is sufficient to produce a 
very perceptible change in his apparent brilliancy. Under 
every circumstance his appearance is considerably brighter 
than that of any star of the first magnitude. 



244 ASTRONOMY. 



Telescopic Appearance, and Time of Rotation. 

195. The most striking feature presented by the planet, 
when viewed with a good telescope, is a system of streaks or 
belts which cross his disk in nearly parallel zones. The 
equatorial zone is usually occupied by a light-colored belt, 
from 25° to 30° in breadth, which is bordered by two nar- 
rower, dark-colored bands, one in the northern and the 
other in the southern hemisphere of the planet. Outside 
of these belts, both toward the north and the south, we 
find an alternating succession of light and dark stripes, as 

shown in Fig. 91, which is 
taken from a drawing by 
Trouvelot. 

The dark belts, which 
seem to be composed of 
dense masses of clouds, are 
very irregular in outline, 
and are subject to frequent 
changes both in form and 
in position. The spaces in- 
tervening between the light 
and the dark stripes are usu- 
ally of a whitish color, but they are often tinged with a 
rose-colored or pinkish hue. 

The contrast between the darker and lighter spaces is 
most strongly marked in the central portions of the disk, 
gradually fading away as we approach the apparent boun- 
dary of the planet. In the polar regions the belts become 
indistinguishable, and the surface of the planet takes on a 
uniform grayish tint. 

These appearances have been accounted for by supposing 
Jupiter to be enveloped by a dense atmosphere ; the rays 
coming from the neighborhood of the apparent edge of the 
planet would have to pass through a greater extent of at- 
mosphere than those from the central regions of the visible 




Fig. 91. Telescopic View of Jupiter. 



PLAKETS AKD SATELLITES. 245 

hemisphere, and would consequently experience a greater 
amount of absorption. It is also possible that the disap- 
pearance of the belts as we approach the polar regions may 
be due in part to perspective ; being seen more obliquely, 
the darker stripes would overlap each other, and thus 
obscure the lighter ones. 

Under favorable telescopic conditions the light-colored 
bands appear slightly mottled, as though covered by a layer 
of shining clouds floating in the planet's atmosphere. 

Other Telescopic Phenomena. 

196. Besides the belts and stripes already described, 
other markings on the surface of the planet are occasionally 
seen. Of these, the most remarkable ones are the white 
and the colored spots, which have recently attracted the 
attention of astronomers. 

The most curious phenomenon of this kind was the 
great red spot which is now just passing away. It made 
its appearance in the southern hemisphere of Jupiter in 
1878, and with occasional disappearances it continued 
visible up to the beginning of 1883. It was carefully ob- 
served by Pritchett, as well as by many other astronomers. 
It was so prominent and its color was so decided that it 
could usually be distinguished even with a small telescope. 

In 1880, its shape was nearly elliptical ; its length, ac- 
cording to Trouvelot, was about 8,000 miles, and its great- 
est breadth was more than 2,000 miles. Its color was of a 
brilliant rosy red, altogether different from the pinkish tint 
that is often seen along the dividing lines of the cloud belts, 
to which reference has already been made. No satisfactory 
explanation of the cause of the spot has been offered. 

Axial Rotation. 

197. Observation shows that Jupiter revolves on an axis 
which is nearly perpendicular to the plane of the ecliptic 
in about 9 hours 55J minutes. 



246 ASTRONOMY. 

Certain phenomena connected with the motion of the 
spots referred to in the last article have led some astrono- 
mers to think that the angular velocity of rotation dimin- 
ishes slightly in passing from the equator towards the poles. 
This diminution, if it really exists, would seem to indicate 
a resemblance to the sun, in which body the rapidity of 
rotation diminishes pretty fast in passing from the equator 
toward the poles. The rapid changes that take place in 
the appearances of the belts and spots indicate the existence 
of forces which can hardly be accounted for, except on the 
supposition that Jupiter's surface is in a semi-molten con- 
dition, at least in his equatorial regions. 

In consequence of the planet's great angular velocity of 
rotation and of his enormous diameter, the actual velocity 
of a point at his equator amounts to more than 27,500 
miles, which is about 27 times as great as that of a point on 
the earth's equator. The resulting centrifugal force is 
therefore sufficiently great to account for the enormous 
compression of the planet. 

Another consequence of the rapid rotation of Jupiter on 
his axis is to make the days and nights on the planet very 
short; the sun is above the horizon for less than 5 hours 
and below it for an equal time. We have no data for de- 
termining the relative changes in these periods due to 
refraction, but there is good reason to believe that there is 
a very dense atmosphere surrounding the planet, and if so 
there must be a considerable increment in the length of the 
day at the expense of the night; the length of twilight on 
the planet must also be so great as to exercise a perceptible 
influence on the relative amounts of daylight and darkness 
at any given point. 

The equator of Jupiter is but slightly inclined to the 
plane of the ecliptic, and as a consequence there is but little 
variation of the seasons ; probably the change is impercep- 
tible at any given place. The days and nights are there- 
fore nearly equal at all seasons of the Jovian year. 



PLANETS AND SATELLITES. 247 

On account of the shortness of the days and the length 
of the year, as compared with those of the earth, the Jovian 
year contains about 10,477 Jovian days. 

Satellites of Jupiter. 

198. Jupiter in his journey around the sun is accom- 
panied by 4 satellites, which revolve about him in orbits 
that are nearly circular. Their motions conform to Kep- 
ler's laws; that is, their orbits are ellipses having one 
focus at the centre of the planet, their radii-vectores de- 
scribe areas which are proportional to the times of descrip- 
tion, and the squares of their times of revolution are pro- 
portional to the cubes of their mean distances from the 
central body. The planes of their orbits are nearly coinci- 
dent with that of the planet, and are consequently but 
little inclined ' to the ecliptic ; they therefore appear to 
move back and forth in straight lines, being seen first on 
one side of Jupiter and then on the other, and never at a 
very great distance from him. 




Fig. 92. Jupiter and bis Satellites. 

Being at different distances from the planet, their greatest 
elongations as well as their apparent times of oscillation 
are different from each other ; sometimes they are seen 
lying in a line parallel to the ecliptic, some on one side and 
some on the other ; sometimes they are all on one side of 
the planet ; and not unfrequently one or more disappear 



248 



ASTRONOMY. 



for reasons yet to be explained. Fig. 92 shows the planet 
and its satellites, three on one side and one on the other. 

A satellite may disappear by passing into the shadow of 
Jupiter, in which case it is said to be eclipsed ; or it may 
disappear by passing behind the body of the planet, in which 
case it is said to be occulted ; or it may disappear, except 
to a good telescope, by passing between the observer and 
the disk of the planet, in which case it is projected upon 
the planet, and its light is confounded with that of the 
planet itself. In the last case, the satellite may.be dis- 
tinguished by means of a good telescope, especially if.it 
passes over the darker portions of the surface. 

The eclipses of Jupiter's satellites are utilized for deter- 
mining longitudes ; it was also from a discussion of the 
eclipses of these bodies that it was first shown that the 
motion of light is progressive and not instantaneous. 

The satellites, though having proper names, are usually 
denoted by the Roman numerals, according to their respec- 
tive distances from Jupiter. The mean distances of the 
satellites from Jupiter, their periodic times, and their 
diameters, are shown in the following 

TABLE. 



Number. 


Name. 


Distance from 
Jupiter in miles. 


Periodic time. 


Diameter 
in miles. 


I 

II 

III... 
IV 


Io,.. 

Europa 

Ganymede. . . 
Callisto 


260.000 

414,000 

661,000 

1.162,000 


Id. 18h. 28m. 

3d. 13h. 15m. 

7d. 3h. 43m. 

16d. 16h. 32m. 


2,352 
2,099 
3,436 
2,929 



It will be seen from the table that the second satellite is 
about the size of our moon, and that the fourth satellite is 
about as large as Mercury, the third one being larger. All 
the satellites are easily seen with a telescope of small mag- 
nifying power, and were it not for the dazzling brilliancy 



PLANETS AHD SATELLITES. 249 

of Jupiter they might even be seen with the naked eye. In 
the more powerful telescopes their surfaces bear traces of 
permanent markings ; from certain changes in their bright- 
ness it has been conjectured that they rotate on their axes 
in the same time that they revolve around Jupiter. 

Eclipses of Jupiter's Satellites. 

199. The eclipses of Jupiter's satellites are analogous to 
eclipses of our moon, but for various reasons they are of 
much more frequent occurrence. On account of the su- 
perior size of the planet and its greater distance from the 
sun his shadow is vastly larger than that of the earth ; fur- 
thermore the dimensions of the satellites are very small in 
comparison with the diameters of the shadow where they 
traverse it; and finally the satellites move in orbits which 
are but little inclined to that of the planet. Hence, it hap- 
pens that the three inner satellites are eclipsed at every 
synodic revolution ; the outer one is generally eclipsed at 
each synodic revolution, bat occasionally it passes either 
above or below the umbra, and so escapes eclipse. 

Taking all the satellites into account, there is an average 
of about 30 eclipses a month, but only a part of them are 
visible from the earth ; at the time of Jupiter's conjunction 
with the sun, the planet and his satellites are invisible 
en account of the dazzling glare of the solar rays-, and 
at the time of his opposition the shadow 7 is turned directly 
away from the earth, and for a considerable time both 
before and after opposition the eclipses are rendered invisi- 
ble by the glare of the planet. The eclipses are seen to 
best advantage when the sun and Jupiter are in, or near, 
quadrature. 

It may happen that two or even three of the satellites are 
eclipsed at the same time, but they cannot all be eclipsed 
at once, on account of the curious relations that exist 
between the motions of the three inner ones. The jovi- 



250 ASTRONOMY. 

centric motions of the first three satellites, that is, their 
motions as seen from the centre of Jupiter are subject 
to the following laws : 

T. The mean sidereal motion of the first added 
to twice that of the third is equal to three times 
that of the second. 

2". The mean longitude of the first, plus twice 
that of the third, minus three times that of the 
second, is equal to 180°. 

If the second and third satellites are eclipsed at the same 
time, the first one must, in accordance with the second law, 
lie between the planet and the sun; or, if the second and 
third lie between Jupiter and the sun, the first will be in the 
shadow of the planet. 

At long intervals it happens that all the satellites are all 
invisible at the same time, some being eclipsed and the 
others being in transit across the bod} 7 of the planet. This 
phenemenon was witnessed by Dawes in. 1843, and by Sir 
W. Herschel in 1802 ; it was again observed in 1868. The 
observations of Dawes show that all the satellites were 
invisible in 1843, for a period of 35 minutes. 

When a satellite passes between Jupiter and the sun it 
casts a shadow upon the planet which may be seen travers- 
ing the disk as a round, or oval, black spot ; to an observer 
placed anywhere along the path thus traversed the sun 
would be totally eclipsed. 

Use in Determining Longitudes. 

200. An eclipse of one of Jupiter's satellites is a phe- 
nomenon which is visible at the same instant in every place 
which has the planet above the horizon ; hence, if two ob- 
servers note the local times of its occurrence at their respec- 
tive places of observation, the difference of these times will 
be the difference of longitude of the two places. 



PLANETS AND SATELLITES. 251 

The Greenwich times of all the eclipses of the satellites 
that are visible during the year at any place on the earth 
are computed and laid down in the Nautical Almanac for 
the use of observers. Hence, an observer has only to find 
his local time at the instant of the occurrence of one of 
these eclipses, to be able to get his longitude either east or 
west from Greenwich. 

The principal difficulty in applying this method is to de- 
termine the exact instant of the eclipse. The phenomenon 
is not instantaneous ; for, the satellite having an apprecia- 
ble magnitude, requires a certain length of time to enter 
the shadow after its advancing limb reaches the umbra, 
and an equal length of time to emerge from the shadow. 
During the former period the light of the satellite is gradu- 
ally growing dim, and the exact time of its disappearance 
will depend upon the character of the telescope used, and 
upon the clearness of the atmosphere at the time of observa- 
tion. A similar difficulty attends the exact determination of 
the time of emergence. Chauvenet says that the error may 
amount, in extreme cases, to a minute of time. If both 
immersion and emersion are observed, which is only possi- 
ble when the planet is at some distance from conjunction 
and opposition, the two errors counteract each other, and 
by combining the results, a fairly approximate value of the 
longitude may be found. It is to be observed that a more 
accurate value for the longitude of a place may be found in 
most cases by the method of lunar distances. 

Velocity of Light. 

201. The progressive motion of light was first shown by 
Eomer, a Danish astronomer, in 1675. In comparing the 
observed with the computed times of the eclipses of Jupiter's 
satellites, he found that they did not correspond ; when 
Jupiter was nearest the earth the observed times were earlier, 
and when he was farthest from the earth they were later 



252 ASTRONOMY. 

than the computed times. He therefore concluded that the 
motion of light was progressive, and not instantaneous, as 
had been previously supposed. 

A discussion of a great Dumber of observations led him 
to the conclusion that the time required for light to travel 
from the sun to the earth is about 8m. 13.3s. If we accept 
the mean distance of the earth from the sun to be 92|- mil- 
lions of miles, Eomer's determination would indicate that 
light travels at the rate 187,500 miles per second, which is 
fairly in accord with the most recent determination of the 
velocity of light ; this, according to Michelson, is 186,300 
miles per second. 

Saturn, h 
Periods. Distances. 

202. Saturn is the fifth planet in order of distance from 
the sun and the next to the largest in order of magnitude. 
He revolves around the sun in a little less than 29-J years, 
his mean distance from that body being about 881 millions 
of miles. 

His synodic period is about 378 days ; hence, he is in op- 
position once in 54 weeks. At opposition he is in the mid- 
dle of his arc of retrogradation, which averages about 6° 48', 
and which is passed over in about 137 days. He begins to 
move westward among the stars a little less than 10 weeks 
before opposition, and continues his westward motion for 
an equal time after opposition. In 1883 his opposition 
period is December 9th, and in 1884 it is December 22d ; 
by the addition of 13 days per year we can find the ap- 
proximate time of opposition for many years. 

The excentricity of Saturn's orbit is .056, and conse- 
quently the planet, when in aphelion, is a little more than 
930 millions of miles from the sun, and when in perihelion 
it is a little less than 832 millions of miles from that body. 



PLANETS AND SATELLITES. 253 

Tke distance of Saturn from the earth may vary from 738 
to 1024 millions of miles. 

Magnitude and Form. Axial Rotation. 

203. The form of Saturn is that of an oblate spheroid, or 
flattened sphere ; its compression is greater than that of 
Jupiter. His greatest, or equatorial, diameter is about 
72,980 miles, and his least, or polar, diameter is 65,580 
miles ; hence, his mean diameter is about 70,366 miles, and 
his volume a little more than 700 times that of our earth. 
Notwithstanding his enormous volume, his mass is only 93 
times that of the earth ; hence, his density is considerably 
less than that of water. 

He rotates on an axis once in lOh. 14m., the plane of the 
planet's equator being inclined to that of the ecliptic in an 
angle of about 28°, and to the plane of the planet's orbit 
by about 26° 49'. Hence, the planet has a succession of 
seasons similar in point of order to our own, but each season 
is nearly 30 times as long as with us. 

Physical Condition. 

204. On account of the great distance of Saturn from 
the earth, it is very difficult to learn much as to its physical 
condition. It is observed to be surrounded by belts similar 
to those of Jupiter, and these belts are found to be parallel 
to the planet's equator ; when the position is such that their 
planes pass through the eye, which happens twice in 29|- 
years, they appear to be straight, but at other times they 
appear, from the principles of perspective, to be elliptical. 

It has been inferred from the varying appearances of the 
belts that the planet has a dense atmosphere loaded with 
clouds. The very small specific gravity, or density, of the 
planet has led many astronomers to believe that the matter 
of which it is composed is intensely heated, but not suffi- 
ciently so to render it self-luminous. 



254 ASTRONOMY. 

The color of the lighter zones of Saturn is of a dull yel- 
lowish hue, the darker bands being gray. As in the case of 
Jupiter, the markings are more distinctly seen in the central 
portion of the disk than at the limb of the planet ; the belts 
entirely disappear in the neighborhood of the poles. 

Rings of Saturn. 

205. The telescope shows us that Saturn is surrounded 
by a broad flat ring, or rather system of rings, whose plane 
is nearly coincident with the plane of his equator. 

This ring, for it will often be convenient to speak of the 
system as a single ring, was first seen by Galileo, but on 
account of the imperfection of his telescope he mistook its 
character. As early as 1610 he announced that Saturn was 
composed of three bodies that almost touched each other. 
Other astronomers described the planet as having ansae, or 
handles. 

It was not till 1056 that Huyghens discovered the real 
nature of the appendage, which he fully described three 
years later. Since the time of Huyghens the character of 
the ring has been carefully studied, and its dimensions and 
divisions have been measured. 

What we have called the ring is in reality made up of 
three concentric rings which lie very nearly in the same 
plane, and which are separated by intervening spaces, unless 
indeed the inner one should prove to be, as astronomers are 
now inclined to believe, an extension of the second or 
middle one. The two outer rings are bright, like the planet, 
but the inner one is obscure or dark, presenting an appear- 
ance that has been compared to a ring of crape. 

This dark ring, which is only visible in a good telescope, 
was first seen by Bond of Cambridge in 1850, and was dis- 
covered independently by Dawes of England only a few 
days later. For convenience of reference, the outer bright 
ring is called A, the inner bright ring B, and the dusky 
ring C, 



PLACETS AND SATELLITES. 



255 



The diameter of the ring system is enormously greater 
than its thickness. In round numbers, the greatest diameter 
of the outer ring is about 170,000 miles, and the breadth of 
the entire system is nearly 38,000 miles ; the thickness of 
the rings is variously estimated from 40 miles up to 250 
miles ; it is probable that the true thickness lies some- 
where between these limits. The relative dimensions of the 
rings in comparison with the equatorial section of the planet 
is shown in Fig. 93. 

Descripttox. — The figure 
shows the rings and equatorial 
section of Saturn in their rela- 
tive dimensions. The ring A, 
whose outer diameter is 168,590 
miles, has a breadth of more than 
10.000 miles, and is probably 
divided into two by a narrow 
line of separation. The ring B 
is separated from the ring A by 
an interval of 1,700 miles; its 
outer diameter is about 145,750 
miles, and its breadth is nearly 
18,000 miles. The ring C is a 
continuation of B, its interior 
diameter being about 92,000 

miles, and its breadth about 8,600 miles. The interval separating the 
inner edge of the dusky ring and the surface of the planet is between 
9,000 and 10,000 miles. 

The rings rotate about an axis which is sensibly coinci- 
dent with the axis of the planet, and in a period which is 
but little greater than that of the planet's rotation period. 
They accompany the planet in his journey around the sun, 
their plane always remaining parallel to itself. 

This plane intersects the ecliptic in two points, which are 
called the nodes of the ring. The heliocentric longi- 
tudes of the nodes are respectively 167J° and 347^-° ; the 
former is called the ascending node, because it is the 
place of the planet where the sun appears to ascend from the 




Fig. 93. Projection of Kings and Planet 
on the plane of his Equator. 



256 ASTRONOMY. 

southern to the northern face of the ring; and the latter is 
called the descending node, because it is the place of the 
planet where the sun appears to descend from the northern 
to the southern face of the ring. 

When the planet is exactly at either of the nodes, the 
plane of the ring passes through the sun, and is only illumi- 
nated on its edge ; at these times the ring is invisible except 
in the most powerful telescopes. Whilst the planet is pass- 
ing from the ascending to the descending node, the sun 
shines continually on the north face of the ring, and 
whilst he is passing from the descending to the ascending 
node, the sun shines continually on the south face of the 
ring. 

The motions and aspects of the ring, as seen from the 
sun, are similar to those of our equator seen from the same 
point of view. The aspect of the ring from the time it 
passes its ascending node till it reaches the descending node 
is similar to that of our earth's equator whilst passing from 
the vernal to the autumnal equinox; the aspect of the ring 
whilst passing back to the ascending node is similar to that 
of the equator in passing from the autumnal to the vernal 
equinox. It is to he borne in mind that the celestial pole of 

the plane of Saturn's ring is 

,5-"'' D N^ only 7° from the north pole 

/ Y of the heavens, a fact which 

/ \ renders the similarity of as- 

pect the more striking. 



/ 



><:' 



V 



--"A 



Explanation.— A is the perihelion 
and B is the aphelion point of Saturn's 
orbit ; N' is the place of the ascending 
and B is the place of the descending node 
of the ring. 



Fig. 94. Illustrating the Motion of The mot i on s and aspects of 

the rings will be understood 
after a careful study of Fig. 94, which represents the pro- 
jection of the orbit of Saturn on the plane of the ecliptic, 



PLANETS AND SATELLITES. 257 

the direction of the vernal equinox being indicated by the 
dotted line below N'S. 

When the ring is at N or N', its plane passes through, the 
sun, and its inclination is such that it passes above D and 
below C. In moving from N to W, in the direction indi- 
cated by the arrow, the sun shines obliquely on the north 
face of the ring ; in moving from W to N, the sun shines 
on the south face of the ring. 

Phases of the Ring. 

206. The orbit of the earth is so small, in comparison 
with that of Saturn, that the direction of the planet as seen 
from the earth is always nearly the same as it would be if 
seen from the sun ; hence, in a general description of the 
phases, or different appearances presented by the ring 
during a sidereal revolution, we may suppose the observer 
to be at the sun. 




Fig. 95. Saturn and his Rings. 

Commencing at N, Fig. 94, the ring is seen edgewise, and 
in a suitable telescope it has the appearance of a bright 
straight line inclined to the direction of the planet's motion 
in an angle of about 26°. As the planet moves on toward 
D, the ring, being seen obliquely, has the form of an ellipse, 
which is very much elongated at first, widening out gradu- 
ally until it reaches D, 90° distant from N; in this position 



258 



ASTRONOMY. 



the minor axis becomes nearly, but not quite, one-half as 
great as the major axis. In this position the northern face 
of the ring and also the northern hemisphere of the planet 
are seen to best advantage. This phase is seen in Fig. 95. 
As the ring moves on toward N', the apparent breadth of 
the ring begins to diminish and continues diminishing till 
the planet reaches W, 180° from N, when it again presents 
itself edgewise, and in a suitable telescope is seen as a 
straight line. 




Fig. 96. Phases of Saturn's Ring. 



After the planet has passed W the ring is again seen as 
an elongated ellipse, which grows broader continually till it 
comes to 0, 270° from N. At this point the phase is simi- 
lar to that at D, except that we now have the best view of 
the southern face of the ring and of the southern hemi- 
sphere of the planet. 

In returning to N, the elliptical form of the ring con- 
tinues to grow narrower, and the ellipse becomes more and 
more elongated till the planet reaches N, when the ring 
phase again becomes a straight line. 



PLANETS AND SATELLITES. 259 

The phases for a complete revolution of Saturn are shown 
in Fig. 96. 

The length of an entire cycle of phases is equal to the 
periodic time of Saturn, or to nearly 29.46 years. The line 
of the ring's nodes, NN', divides the orbit of the planet into 
two unequal parts, and because "the areas are proportional 
to the times," the corresponding times are different. The 
time required for the planet to move from the ring's ascend- 
ing to its descending node is about 15.75 years, and the 
time required for him to pass from the descending to the 
ascending node is about 13.71 years. Hence, the sun shines 
continuously on the northern face of the ring for 15f years, 
and then on the southern face for nearly 13| years. 

The last passage of the planet through the ascending 
node of the ring took place on the 18th of May, 1862, and 
his last passage through the descending node was on the 
14th of February, 1878; the planet will return to the 
ascending node on the 29th of October, 1891. The south- 
ern face of the ring will be most favorably seen in 1885. 

Disappearance of the Ring. 

207. In the last article the observer was supposed to be 
at the sun ; the phenomena there described are somewhat 
modified by the fact that we see them from the earth, and 
this is more especially the case during the time that the 
plane of the ring intersects the earth's orbit, 

This plane, which is parallel to the line of nodes of the 
ring, occupies nearly a year in sweeping across the orbit of 
the earth, and in that interval the ring may be so situated 
as to pass between the earth and the sun more than once, 
in which case the ring will disappear because its illuminated 
face is turned away from us. 

The number of disappearances and the duration of each 
will depend on the position of the earth when the plane of 
the advancing ring strikes her orbit. The nature of these 



260 ASTRONOMY. 

disappearances and their manner of occurrence will be un- 
derstood from the following description of the disappear- 
ances that took place about the time of the last passage of 
the planet through the ascending node of the ring in 1862. 

■jK - Ad 



H 



7° 



Fig. 97. Disappearance of Rings. 



Explanation. In Pig. 97, AB is the earth's orbit ; CD, the projection of a part 
of the orbit of Saturn on the plane of the ecliptic ; N is the ascending node of the 
ring ; NS, the intersection of the plane of the ring with the ecliptic ; and the paral- 
lel lines are different positions of this line. The plane of the rings is inclined so as 
to pass above B and below A ; the observer is supposed to be looking on the north 
face of the ring. 



At the time the plane of the ring struck the earth's orbit 
at A, the earth was moving toward a ; on the 23d of No- 
vember, 1861, the earth met the plane of the advancing ring 
at a, passed through it from the south to the north side, 
and the ring disappeared ; the sun continued to shine on 
the southern side, and the earth remained on the northern 
side till February 1, 1862, when the earth overtook the 
plane of the ring at b, passed through it from the north to 
the south side, and the ring reappeared. It was invisible 
for 70 days. 

The sun and the earth then remained on the south side 
of the ring, and the ring continued visible till May 18, 
1862, at which time the earth was at c and Saturn at N ; 
at this time the plane of the ring passed through the sun, 
and then the northern face began to be illuminated, the 
earth being on the southern side, and the ring again disap- 
peared ; the plane of the ring continued to lie between the 
earth and the sun till August 13, 1862, when the earth met 



PLANETS AND SATELLITES. 261 

it at d, passed through it from the south to the north side, 
and the ring again reappeared. At this disappearance it 
was invisible for 87 days. 

The earth and the sun being now on the same side of the 
plane of the ring, no further disappearance took place till 
the next passage of the plane of the ring across the earth's 
orbit, which happened in 1877-8. 

Every time that the plane of the ring sweeps across the 
earth's orbit there must be at least one disappearance in 
consequence of the plane of the ring passing between the 
earth and the sun, and there may be as many as three such 
disappearances. When a disappearance arises from the 
cause just mentioned the ring may remain invisible for 
several months ; when it is at the node, in consequence of 
the passage of its plane through the sun, it only remains 
invisible for a short time. 



Physical Character of the Rings. 

208. That the rings A and B are opaque bodies is shown 
by the fact that they cast shadows on the body of the planet. 

The ring C is partially transparent, for the outline of the 
planet can be seen through it. 

The old idea that the rings are solid bodies has long since 
been abandoned, it having been demonstrated that such a 
supposition is incompatible with the laws of mechanics; 
furthermore, the idea of a solid ring is incapable of being 
reconciled with the changes that have been observed in the 
rings, that is, changes of form, indicated by the variations 
of the shadings and other markings that are sometimes 
noticed. 

For a time it was thought by some astronomers that the 
rings were fluid ; but this theory was shown to be erroneous 
by Maxwell in his prize essay written in 1857. He showed 
that the only tenable hypothesis in regard to their consti- 
tution is that they are made up of myriads of independent 



262 ASTKONOMY. 

bodies revolving around the planet like so many satellites 
and subject, like other satellites, to multitudinous pertur- 
bations. These revolving satellites are so small as to be in- 
visible in the most powerful telescope, and so numerous as 
to give the impression of a continuous body. According to 
this view, we may regard the ring as composed of satel- 
lites more widely separated than in the other rings, and 
possibly less capable of reflecting light. 

Eecent observations on the form of the shadow which the 
ball of the planet casts on the surface of the rings have led 
some astronomers to believe that the rings are not of uni- 
form thickness ; that is, that their faces are not parallel 
planes. Trouvelot, who has devoted a great deal of study 
to the subject, is of the opinion that the ring A is of uni- 
form thickness, and that the ring B is thickest at its outer 
limit, growing thinner toward the sun ; it is highly prob- 
able that the same law of diminution holds good with regard 
to the ring C. 

The brightest part of the entire ring system is the outer 
zone of the ring B ; in approaching the sun the brilliancy 
slowly diminishes to its inner zone. The ring A is less 
brilliant than the ring B, and, as we have already seen, the 
ring is far less brilliant than either. 

Satellites of Saturn. 

209. Saturn has 8 satellites, 7 of which revolve around 
him in orbits that are nearly coincident with the plane of 
his rings, and consequently with the plane of his equator ; 
the orbit of the other one is inclined to the plane of the rings 
in an angle of about 10°. Five of them were discovered 
in the 17th century, two in the 18th century, and the other 
one, the seventh in order of distance from Saturn, was not 
known till 1848, when it was discovered by Bond of Cam- 
bridge, and independently by Lassell of England. 

The satellites of Saturn are subject to eclipse, but in con- 
sequence of the great inclinations of their orbits to the 



PLANETS AND SATELLITES. 



263 



plane of the ecliptic, their eclipses are of less frequent oc- 
currence than those of Jupiter. When the ring is seen 
edgewise, the first 7 appear to move back and forth with a 
shuttle-like motion, and have sometimes been seen moving 
along the bright line of the ring like beads on a string. 
When the ring is seen obliquely the satellites appear to be 
scattered as shown in Fig. 98. 




Fi£. 



Saturn and his Satellites. 



The names, distances from Saturn, and diameters of the 
satellites, so far as known, are given in the following table 
taken from Chambers' Astronomy. 



TABLE. 



Number. 


Name. 


Distance from 

Saturn in 

miles. 


Approximate Sidereal 
diameter in Period in 
miles. days. 


I 

II 

III.... 

IV 

V..... 

VI 

VII.... 
VIII... 


Mimas 


120,800 
155,015 
191,248 
245,876 
343,414 
796,157 
1,006,656 
2,313,835 


1,000 0.94 


Enceladns 


? 

500 

500 

1,200 

3,300 


1.37 
1.88 ! 
2.73 
4.51 
15.94 


Tethys 

Dione 

Rhea 

Titan 


Hyperion.. 

Iapetus 


? ! 21.29 
1,800 79.33 









Comparison of Jupiter and Saturn. 

210. The planets Jupiter and Saturn resemble each 
other in many respects. Both are large planets with very 
small densities, the former being the largest and the latter 



264 ASTRONOMY. 

the next largest of all the planets ; they both revolve on 
their axes in very short periods of time, about 10 hours, and 
both are very much flattened at the poles ; both have dense 
atmospheres loaded with enormous clouds, which are thrown 
into belts by currents parallel, or nearly so, to their equa- 
tors ; and it has been suspected that both are, by virtue of 
internal heat, at a temperature bordering on incandescence. 

Uranus, ty, or 6 . 
Discovery, Distances, and Periods. 

211. The planets heretofore described have been known 
from the most ancient times. Uranus, which is the seventh 
planet in order of distance from the sun and the fourth in 
order of magnitude, was not known till 1781, when it was 
discovered by Sir William Herschel, whilst examining some 
small stars in the Constellation Gemini. 

He at first supposed that it was a comet, and in a paper 
presented to the Royal Society he described it as such. 
After considerable discussion it was found to be a planet, 
and was named by its discoverer the Georginm Sidus, in 
honor of his royal patron George III. Lalande suggested 
the name Herschel, which was afterward changed, at the 
suggestion of Bode, to Uranus, by which name it is now 
universally recognized. The symbol #, which was adopted 
to designate the planet, was simply the initial letter of Her- 
scbel's name, with a planet suspended from the cross-bar; 
but this symbol is passing out of use, being replaced by 
the less expressive sign $ . 

Uranus revolves around the sun in 40,687 days, or a little 
more than 84 years, its mean distance from that body being 
about 1,771,000,000 of miles. The excentricity of its orbit is 
a trifle less than that of the orbit of Jupiter, in consequence 
of which the planet approaches to within 1,689,000,000 
miles of the sun, and recedes from that body to a distance 
1,853,000,000 of miles. Its changes of distance, both from 



tLAtfETS AND SATELLITES. 265 

the earth and from the sun, though enormous in them- 
selves, are so small in comparison with the planet's mean 
distance from either, that they can have but little effect on 
the visibility of the planet, or on its relative supply of light 
and heat. Its synodic period is no more than 370 days. 

Magnitude, Rotation, and Physical Condition. 

212. The diameter of Uranus is about 31,700 miles, and 
although it was reported by Madler to be flattened, the 
statement is now doubted by the ablest observers. Its vol- 
ume is about 64 times that of the earth, but its mass is only 
14 times as great. Hence, its density is only 1.25, that is, 
1£ times that of distilled water. It is not known whether 
the planet rotates on an axis, although it is probable that 
it does so, its axis being perpendicular to the planes of the 
orbits of the satellites, yet to be described. Of its physical 
condition we know little or nothing. 

Satellites of Uranus. 

213. The satellites of Uranus are only visible in a pow- 
erful telescope and under favorable circumstances. Four 
are certainly known to exist, and others have been sus- 
pected. Two of the four were discovered by the elder 
Herschel, and have been studied by various observers. The 
other two were discovered by Lassell in 1852, under the 
pure sky of Malta. 

Sir William Herschel announced the existence of six satel- 
lites, two of which are identical with those already spoken 
of, but the other four, if they have an actual existence, are 
not recognized at the present time. Mr. Lassell, during 
his residence at Malta, examined the region of the heavens 
about Uranus with great care, and as the result of his 
observations he says: " I cannot resist the conviction that 
Uranus has no other satellite except four visible with my 
eye and optical power. In other words, I am fully persuaded 
12 



266 



ASTRONOMY. 



that either he has no other satellite than these four, or if he 
has, they remain yet to be discovered." 

According to Newcomb the planes of the orbits of these 
satellites are inclined to the ecliptic in an angle of 97° 51', 
or nearly 98°. If their planes of revolution were ever co- 
incident with the plane of the ecliptic they must have 
been turned over till perpendicular to the ecliptic, and then 
8° further. Looking down upon the satellites from the 
north side of the ecliptic they appear to move from east to 
west ; that is, their motion is retrograde. It is but reason- 
able to suppose that rotation of the planet is in the same 
direction, and if so, this is certainly a strong point against 
the truth of the nebular hypothesis. The satellites in 
order of distance, their names, and periodic times, are given 
in the following table taken from Chambers' Astronomy. 

TABLE. 



Number. 


Name. 


Periodic time 
in day§, 


Mean distance 
in miles. 


r 


Ariel 


2.52 

4.14 

8.71 

13.46 


122,849 
171,229 
280,869 
375,648 


II 


Umbriel 


Ill 

IV 


Titania 

Oberon 





Neptune, f . 
Its Discovery. 
214. The eighth planet in order of distance from the 
sun, and the third in magnitude, is called Neptune. It 
was first observed on the 23d of September, 1846, by a Ger- 
man astronomer named Galle, but its place in the heavens 
had been indicated to within less than a degree by Le Ver- 
rier; to this astronomer, therefore, and to the English 
mathematician Adams, who also predicted the place of the 
planet to a great degree of accuracy, must be assigned the 
honor of the discovery. 



PLANETS AND SATELLITES. 



267 



For many years previous to 1846 irregularities had been 
noticed in the motion of Uranus, which could only be ex- 
plained by supposing the existence of an exterior planet, 
and the minds of scientific men had been directed toward 
the solution of the problem as to whether such a planet did 
exist, and if so, where it was to be found. 

The nature of the disturbances of Uranus, which led to 
the discovery of Neptune, will be understood from the 
diagram, which shows the relative positions of Uranus and 
the then unknown planet Neptune, from 1781 to 1840. 



Explanation. The inner cir- 1822. 

cle represents the orbit of Uranus, 
and the outer circle that of Nep- 
tune, the sun heing a£ S. The 
corresponding positions of the 
two planets are indicated by the 
corresponding dates, and the di- 
rections of Neptune's attraction 
is shown by the arrows. 

In 1821, at which 
time Uranus and Nep- 
tune were nearly in con- 
junction, Bouvard pub- 
lished his tables of 
Uranus, basing them on 
an orbit of the planet 
which harmonized with 
the observations that 

had been made between 1781 and 1820. After the publica- 
tion of these tables it was soon found that the observed 
places of the planet did not conform to those given by the 
tables, and as the time after 1822 increased, these discrep- 
ancies became continually greater. 

Adams began his investigations in 1843, and in 1845 he 
sent to the Astronomer Eoyal provisional elements of a 
planet which he thought would account for the perturba- 
tions of Uranus, but no active search was made to verify 




Pig. 99. Relative positions of Uranus and 
Neptune. 



%68 ASTROXOMY/. 

his predictions. In the latter part of 1845 Le Vender pub- 
lished a memoir to show that the perturbations of Uranus 
were not due to the sole action of Jupiter and Saturn, and 
in June, 1846, he published a second memoir to show that 
an exterior planet was the cause of the unexplained part of 
the disturbance. He assigned the elements of the orbit of 
such a planet, as Adams had done a few months previously. 
In the following August he published a third memoir, in 
which be indicated the probable place of the disturbing 
planet in the heavens, which was very nearly the same as 
that which had been pointed out by Adams. 

On the 23d of September, Encke of Berlin received a 
letter from Le Verrier, requesting him to co-operate in 
the discovery of the planet. That very*night, Dr. Galle, 
Encke's assistant, turned his telescope to the place indicated, 
and soon discovered what seemed to be a star of the eighth 
magnitude, which was not laid down on Bremiker's chart of 
that region. On the following night he found that it had 
changed position, a discovery which made it evident that it 
was in reality the planet sought for. It is unnecessary to 
say that this discovery, which must ever redound to the 
honor of both Le Verrier and Adams, is one of the most 
brilliant achievements of modern science. 

Distance, Periods, Magnitude, and Physical Condition. 

215. The mean distance of Neptune from the sun is 
about 2,775 millions of miles ; his orbit is but little excen- 
tric, his distance from the sun at perihelion being 2,750 
millions of miles, and at aphelion 2,800 millions of miles. 

His periodic time is nearly 164J years, and his synodic pe- 
riod is only 367 h days; that is, he moves forward among the 
stars in a year no farther than the earth does in %\ days. 

The diameter of Neptune is 34,800 miles, so that his 
volume is 85 times that of the earth. His mass is only 17 
times the mass of the earth ; hence, his density but little 
greater than that of water. 



PLANETS AND SATELLITES. 269 

We know little or nothing of the physical character of 
the planet. It probably revolves on an axis, but we are 
ignorant of the time of his rotation and of the position of 
his axis of rotation. 

Neptune's Satellite. 

216. Neptune has one satellite which revolves around 
the planet in a period of 5.877 days, and in an orbit whose 
inclination to the ecliptic is a little more than 145°, that is, 
the motion of the satellite, as seen from the north side of 
the ecliptic, is from east to west, or retrograde. The plane 
of the orbit of the satellite is turned over, so to speak, with 
respect to that of the planet, and if we suppose the axial 
rotation to correspond in direction with that of the motion 
of the satellite, we are thereby furnished with a still 
stronger argument against the nebular hypothesis than in 
the case of Uranus. The mean distance of the satellite 
from Neptune is about 220,000 miles. 

Comparison of Uranus and Neptune. 

217. We have seen that the first six planets taken in pairs 
are somewhat closely allied in their physical conditions ; 
thus, Mercury and Venus resemble each other in many 
respects ; the Earth and Mars are more strikingly alike,, 
and even Jupiter and Saturn have many peculiarities in 
common. In like manner Uranus and Neptune may be 
compared ; they agree in the fact that neither presents any 
peculiar markings by which its time of rotation can be 
determined ; the strongest point of resemblance, however, 
consists in the peculiarity of the motion of their satellites, 
the plane of motion in both cases being overturned, as it 
were, so that the apparent motions of the satellites are 
retrograde. We know little or nothing about the physical 
condition of either. 



XL COMETS AND METEORS. 

Comets Members of the Solar System. 

218. Besides the bodies already described, hundreds of 
other bodies called comets are recognized by astronomers 
as belonging to the solar system. 

They differ from the planets in many respects: their 
orbits are greatly elongated and are often highly inclined to 
the plane of the ecliptic ; in fact, they make every possible 
angle with that plane ; their motions are sometimes direct 
and sometimes retrograde ; they generally contain but little 
matter, and are often, perhaps generally, surrounded by 
nebulous envelopes and accompanied by trains of similar 
nebulous matter, though in the latter respect there is a 
wide difference between different individuals. 

They resemble the planets in conforming to the New- 
tonian law of universal gravitation : their orbits are always 
conic sections, haviug one focus in each case at the 
sun ; the radius-vector of each describes areas which are 
proportional to the times of description, but in consequence 
of their extreme tenuity they are greatly disturbed in 
their motions by the attractions of the planets, and they 
are often thrown from their normal orbits and forced to 
take up new ones. 

Definition. 

219. The word comet, which is derived from the Greek, 
signifies a hairy or bearded star, that is, a star with a nebu- 
lous surrounding that resembles a bunch of hair, or a 
beard. 



COMETS AND METEORS. 271 

Before the true character of comets was discovered, they 
were objects of popular dread ; they were considered as 
omens of the wrath of Heaven and as " harbingers of war 
and famine, of the dethronement of monarchs and the dis- 
solution of empires ; " nor have these popular notions 
entirely disappeared, for even at the present day, the 
appearance of a comet is regarded by many with fear and 
apprehension. 

Elements of a Comet's Orbit. 

220. It has been' stated that the orbit of a comet is 
some one of the conic sections. Of course no comet can 
return periodically unless its orbit is an ellipse ; bat it 
usually happens, even when a comet's orbit is elliptical, 
that its excentricity is so great that we may regard that 
portion of it along w r hich the comet is visible as sensibly 
coincident with a parabola having the same focus, and the 
same perihelion distance. 

Hence, when a new comet appears, astronomers are in the 
habit of regarding its orbit as a parabola, inasmuch as the 
labor of computing the elements of a parabolic orbit is much 
less than is required for computing the elements of an ellip- 
tical orbit. The parabolic elements thus found are gener- 
ally sufficient to show whether the comet in question cor- 
responds to any one that has appeared before, and if so an 
elliptic orbit may then be computed. If the parabolic ele- 
ments do not indicate the identity of the comet with any 
one previously observed, they will be sufficient to enable us 
to predict the motions of the body until a sufficient num- 
ber of observations have been made to determine a more 
accurate orbit. 

The elements of a parabolic orbit are five in number, and 
these may be determined from three good observations of 
the body taken at intervals of one or two days. They are 
as follows : 



272 ASTEOKOMY. 

T. The heliocentric longitude of the ascending 
node : 

2°. The inclination of the plane of the orbit to that 
of the ecliptic ; 

3°. The heliocentric longitude of the perihelion ; 
Jf . The epoch, or time, of perihelion passage; and, 
5°. The perihelion distance, or the distance from 
the sun at the epoch. 

The Number of Comets. 

221. The number of comets that have been noticed and 
recorded is very great, amounting to many hundreds. Of 
these only the most conspicuous ones had been observed up 
to the time of the discovery of the telescope, and even they 
can hardly be said to have been observed in the modern sense 
of that term. Within a few years, however, great attention 
has been paid to cometary astronomy, and already from tivo 
to three hundred have been catalogued, that is, the elements 
of their orbits have been determined, with greater or less 
accuracy, and the results have been registered for future 
reference. 

Besides those that have been catalogued in modern times, 
great numbers must have escaped notice either from their 
minuteness, or because their paths were in that portion of 
the heavens which happened to be illuminated by the sun at 
the time of their nearest approach to the earth and conse- 
quently were above the horizon only in the daytime. 

On an average, when long periods are considered, there 
are 26 or 27 comets per century that are visible with the 
naked eye. The number of telescopic comets is vastly 
greater. 

General Description of a Comet. 

222. Comets differ so much in appearance that no sin- 
gle description is applicable to them all. In general* how- 



COMETS AND METEORS. 273 

ever, a comet may be said to consist of three parts : 1°, a 
shining stellar point called the nucleus ; 2°, a surround- 
ing mass of nebulous matter called the coma ; and 3°, an 
extension, or prolongation, of the coma called the tail. The 
nucleus and coma together make up the head of the comet. 

The nucleus, which appears to be composed of matter in 
a state of incandescence, and which may or may not be 
solid, varies greatly in brilliancy in different comets. 
Sometimes it shines like a star of the first magnitude, 
sometimes it is so faint as hardly to be discernible, and in 
some cases there is no trace of a luminous centre. Some- 
times the stellar point is sharp and clear, but more fre- 
quently it is hazy and badly defined. 

The coma consists of a vapor-like mass of matter some- 
what condensed toward the nucleus, but greatly diffused 
toward its outer surface; its outline is very indistinct, and 
at a little distance from the nucleus it is so tenuous that 
stars may be seen through it. Its bulk is often enormous, 
but the quantity of matter that it contains is very small, as 
is shown by the readiness with which it yields to the dis- 
turbing forces of the planets and the little influence it ex- 
erts upon them in return. The extreme tenuity of the 
coma is shown by its enormous bulk in comparison with its 
mass. 

The tail, which is even more tenuous than the coma, is 
turned away from the sun, and in many instances it extends 
to an enormous distance from the nucleus ; in other cases 
it is comparatively insignificant, and not infrequently it is 
totally wanting. In no respect do comets differ more from 
each other than in respect to this appendage; the great 
comet of 1843 had a tail that extended over an arc of 65°, 
and which was not less than 150,000,000 of miles in length, 
while the bright comets of 1665 and 1682 are described by 
Cassini as being round and well-defined like Jupiter. Some 
brilliant comets have very short tails, and some faint comets 
have very long ones. 



274 ASTRONOMY. 

Some comets have been noticed with several tails, or di- 
verging streams of nebulous matter: the great comet of 
1774 is described as having had six tails spreading out like 
a fan and covering an angular space of 30° ; the smaller 
comet of 1823 had two tails making an angle with each 
other of 160°, the brighter and principal one being directed 
away from the sun, while the lesser one lay in nearly an op- 
posite direction. It is to be observed that telescopic comets, 
as a general thing, have no tails, or at most only short ones ; 
their bodies usually appear as simple spherical or slightly 
elongated masses of vapor. 

Brilliancy and Visibility. 

223. Comets have every degree of brilliancy, from those 
magnificent specimens that are visible with the naked eye 
in broad daylight down to the almost evanescent wisps of 
nebulous matter that can only be seen with a powerful 
telescope. 

Many comets have been seen in the daytime : the great 
comet of 1843 was thus seen when it was within 2° of the 
sun ; the great comet of 1861 was seen just before sunset; 
the great comet of 1882 was also seen in close proximity 
to the sun ; and to these examples many others might be 
added. 

It has often happened that comets have been seen during 
the time of a solar eclipse : such an event occurred during 
the eclipse of 63 B.C. ; in 418 A.D. a large comet was 
seen during the eclipse of that year ; and also during the 
eclipse of 1882, which was observed by Lockyer and others 
in Egypt, a comet was seen and photographed. 

It has already been stated that the average interval be- 
tween the appearances of comets, large enough to be seen 
with the naked eye, is about 4 years. Some of them re- 
main in sight but a few days, and others are visible for 
longer periods, up to several months. Not to go too far 



COMETS A^D METEORS. 275 

back into astronomical history, we may give a few examples 
of recent comets that remained visible either to the naked 
eye or to the telescope for long periods of time. 

The great comet of 1811, one of the most conspicuous of 
modern times, remained visible for 17 months ; the bright 
comet of 1815 was visible for nearly 6 months ; the comet 
that was first seen in the latter part of 1825 was visible for 
nearly a year ; the great comet of 1813 was observed for 7 
weeks ; Donati's comet, one of the finest comets of the cen- 
tury, was a conspicuous object in the heavens during the 
autumnal months of 1858, and did not finally disappear in 
the telescope till the following March ; and finally the 
remarkable comet of 1882 was visible to the naked eye for 
many weeks. 

Mass and Tenuity. 

224. It has been stated that the smallness of a comet's 
mass is shown by the great disturbance it experiences from 
the action of the planets ; the following instance will illus- 
trate the subject more fully than further description : 

A comet appeared in 1770, which was found to move in 
an elliptical orbit, with a periodic time of about 5|- years ; 
it is known in history as Lexell's comet. The wonder was 
why it had never been seen before, and so great was the 
interest of astronomers in the matter that the French 
Institute offered a prize for a complete investigation of its 
history. As a result of this investigation, it was found that 
it had been greatly disturbed by the attraction of Jupiter. 

In tracing its orbit backward, it was found that in 1767, 
it had come within the influence of Jupiter, in whose 
neighborhood it had remained for several months, and 
when it finally left that planet it had been thrown into a 
5-J-year orbit. Previously it had moved in a 50-year orbit, 
whose perihelion distance was nearly equal to that of 
Jupiter, and for this reason it had never been seen before, 



276 ASTKOtfOMF. 

Strangely enough, the comet at a later period again fell in 
with Jupiter, and after being detained for a few months in 
that neighborhood it was thrown into a 20-year orbit, with 
a perihelion distance of between 200 and 300 millions of 
miles, and unless it is again disturbed it will, on account 
of its great distance, remain forever invisible to us. Dur- 
ing all these changes in the path of the comet, the orbits of 
Jupiter's satellites were not changed in any perceptible 
degree. Laplace concluded that the mass of this comet 
could not exceed the 5,000th part of that of the Earth. 
The curious history of this comet suggests an explanation 
of many strange anomalies that have been observed in this 
class of bodies. 

As illustrations of the extreme tenuity and almost perfect 
transparency of cometary bodies, the following cases may 
be mentioned : In 1824 Struve saw a star of the twelfth 
magnitude when it was so near the centre of an intervening 
comet that it could not have been more than 2" from the 
densest portion, and yet the star experienced no sensible 
diminution in brightness. Again, in 1829, the same 
astronomer saw what he thought to be a comet with a 
stellar nucleus, but which turned out to be only a star of 
the eleventh magnitude shining through the head of the 
comet. In October, 1874, the comet discovered by Miss 
Mitchell of Nantucket passed over a star of the fifth mag- 
nitude so centrally that it could not be decided on which 
side the nebulosity was greatest, even with a magnifying 
power of 100, and yet the light of the star was not 
perceptibly enfeebled. 

Mr. A. B. Biggs, in writing from Tasmania of the great 
comet of 1882, says : 

" On Monday evening at 10 o'clock I perceived a minute 
star (ninth magnitude) in the advancing edge of the 
comet's coma, which I foresaw would be crossed centrally 
by the nucleus — a rare opportunity which I determined not 
to miss, At 11 o'clock the star was fairly in the centre of 



COMETS AKD METEORS. 2?? 

the nucleus. The nucleus was perfectly transparent. I 
watched the star until it had well crossed, and never lost 
sight of it even when a slight atmospheric haze obscured 
the comet itself. The light of the star w T as not even 
sensibly diminished, except so far as being seen upon the 
light background of the comet. v 

Prof. Young, in a recent lecture, said: " Encke's comet, 
when I was observing its spectrum, passed so centrally over 
a star that I thought something had happened, because 
I saw that there was a stellar spectrum ; but ten minutes 
afterward it had passed by. Yet the star was not dimmed 
at all. Afterward I had a candle placed so that its light 
should shine on the object-glass of the telescope, making 
the field of view about as bright as the comet was, and I 
found this light dimmed the star as much as the 50,000 
miles of comet did. A comet is a mere airy nothing." 

It may be observed that the slightest fog or haze is suffi- 
cient to obscure a star of the magnitude referred to. The 
facts just given suggest the idea that the nuclei of bright 
comets may not be solid, nor even very dense bodies. 

Appearance of the Tail. 

225. As we have already seen, the appearances presented 
by the tails of different comets are exceedingly diverse. 
The normal or average type, however, consists of a slightly 
diverging brush of light, extending away from the sun, 
being brightest near its borders and darkest along the cen- 
tral line or axis. 

The dark shade of the axial line can be accounted for by 
supposing the tail to be a greatly elongated and hollow 
paraboloidal envelope, having its focus at the centre of the 
nucleus. The portion of this envelope which is turned 
toward the sun is in fact a part of the coma, and its pro- 
longation beyond the nucleus is the real tail. 

In viewing such an envelope it is easily seen that the 



278 ASTRONOMY. 

portions along the axis would appear darkest, while those 
near the border would seem to be brightest. Let A B, Fig. 
100, represent a cross-section of such an envelope, made by 
a plane perpendicular to its axis; and 
suppose the space between the two cir- C , 

cles to be filled with diffused luminous /^^J~^ K 

matter. It is evident that a line of (=^- ^ \r\ 
vision, CD, through the centre, 0, will A ^j o| 11§ B 
contain fewer luminous particles than y^^ I ^>m/ 
one through EF, and consequently \ } ] $( 

to an eye situated below the section it ft 

will appear to be brighter at F than it y *p 

does at D. . 

Fig. 100. Ideal Cross- 
When We COme to the Study Of section of a Comet's Tail. 

Donati's comet we shall see that the 

tail is made up of several such hollow envelopes, a fact that 

will somewhat modify the above conclusion, without in 

any manner impairing its validity. The differences that 

are noticed in the tails of different comets and in the tails 

of the same comet at its different returns will be considered 

hereafter. 



Curvature of Comets' Tails. 

226. The tails of most comets appear to be curved some- 
what like a Turkish scimetar, the concavity of the curve 
being turned toward that part of the orbit which has already 
been traversed by the comet. The bending, as a general 
rule, takes place in the plane of the orbit, and as a conse- 
quence the apparent curvature will depend not only upon 
the actual amount of bending, but also upon the position 
from which it is viewed ; if seen from a point in, or nearly 
in, the plane of the comet's orbit, the tail will appear nearly 
straight; if seen obliquely, the amount of curvature will 
obviously vary with the degree of obliquity. 

The curved form of a comet's tail is well shown in Fig. 



COMETS AtfD METEORS. 279 

101, which represents the great comet of 1858, usually 
known as Donati's comet. 




Fig. 101. Donati's Comet, 1858. 

The explanation of this curved appearance depends on 
a theory that has been advanced to account for the forma- 
tion of the coma and tail. The theory in question supposes 
that a portion of the comet becomes vaporized in approach- 
ing the sun, and that the vapors thus formed are repelled 
both by the comet and by the sun. By virtue of the comet's 
repulsion these vapors rise in the form of envelopes sur- 
rounding the comet, and by virtue of the sun's repulsion 
they are elongated and driven away from the nucleus to 
form the tail. 

The manner in which the successive envelopes are formed 
and driven off is shown in Fig. 102, which represents the 
head and a portion of the tail of Coggia's comet of 1874, as 
drawn by Trouvelot. 



280 



ASTRONOMY. 



This theory being accepted, the curvature of the tail is 
easily explained. The particles driven off at any instant, 




Fig. 102. Coggia 1 * Comet, 1874. 



moving under the action of inertia and the sun's repellent 
force, will describe paths which, for the purpose of descrip- 
tion, we may regard as normal to the comet's orbit. Of all 
the particles driven off during a given period, those first 
repelled will have moved to the greatest distance from the 
orbit, those next in order will have moved to a less distance, 
and so on to the last, which will have moved to the least 
distance ; it is obvious that the aggregate appearance of all 
these points at any time will be similar to that shown in 
Fig. 101. 

The explanation just given is not dissimilar to that which 
would account for the formation of the curved and ever- 
widening train of smoke that is seen to follow a moving 



COMETS AKD METEORS. 281 

steamer. The smoke emitted at each instant is forced up- 
ward by the buoyant effort of the air, expanding as it rises, 
until it finally becomes so tenuous as to be invisible. The 
aggregate appearance of all the smoke emitted has at any 
instant a shape that is not unlike the curved tail of a comet, 
lying outside of, and curved toward the path of the steamer. 

Volume of some Comets. 

227. The famous comet of 1811 was one of the largest of 
which we have any record ; the diameter of its head was 
about 600,000 miles, and its tail extended to a distance of 
more than 60,000,000 of miles, so that its entire volume was 
nearly or quite as great as that of the sun itself. The great 
comet of 1769 was 500,000 miles in diameter, and its tail 
not less thnn 50,000.000 of miles in length. As we have 
already stated, the great comet of 1843 had a tail whose 
length was 150,000,000 of miles. 

In this connection several important questions arise : 
first, is it possible that the attraction of the head of the 
comet is sufficient to gather up all the matter that is thrown 
off to form the tail ? secondly, if not, would the quantity^ of 
matter thus expended bear any appreciable proportion to 
that which remained ? and thirdly, if the matter were not 
gathered up and condensed upon the body of the comet, 
would it condense by itself so as to form a new comet ? 

Varying Dimensions of the same Comet. 

228. It is a well established fact that some comets actu- 
ally diminish in bulk as they approach the sun, and expand 
again as they recede from that body. In other cases the 
change observed is exactly the reverse. These facts have 
suggested the idea that the condition of the matter in these 
two classes of comets is in some way quite different. The 
former set of facts has suggested the idea of a medium 
growing denser toward the sun, which acts by its pressure 



2&2 AStROKOMY. 

to condense the cometic matter in its approach to that body 
and permitting it to expand when receding ; the latter set 
of facts would seem to render this idea untenable. 

Grant, in his History of Physical Astronomy, says : " A 
more probable explanation has been suggested by Sir John 
Herschel. According to that astronomer, as the comet ap- 
proaches perihelion the action of the solar heat will be con- 
stantly transforming the nebulous matter of which it is 
composed into the condition of a transparent invisible gas ; 
and as this process necessarily takes place at the exterior of 
the nebulosity, where the solar rays impinge, the imme- 
diate consequence will be a diminution of the volume of the 
comet. After the passage of the perihelion the radiation of 
heat from the surface of the more condensed portion of the 
comet will not be sufficiently compensated by the solar heat 
received, and the difference of temperature thence arising 
will occasion a precipitation on the surface of the nebulous 
matter suspended in a gaseous state in the atmosphere of 
the comet. This precipitation of nebulous matter will con- 
tinue to go on under the influence of the cooling process 
occasioned by the increasing distance of the comet from the 
sun, and the manifest result will be a rapid enlargement of 
the visible dimensions of the comet." 

Source of a Comet's Light. 

229. The question has been raised whether comets shine 
by their own or by reflected light. Arago undertook to set- 
tle the matter by experiment, making use of the optical 
principle that light emanating from a self-luminous body is 
not polarized, whereas reflected light is always more or less 
polarized. He found that cometic light was partially 
polarized, and from this he inferred that comets are opaque 
bodies shining by reflected light. This conclusion is obvi- 
ously illogical, though the conclusion arrived at is in most 
cases probably true. It is plain that a comet might be self- 



COMETS AND METEORS. 283 

luminous and yet reflect a certain amount of solar light, 
and this, mingled with emitted light, might give rise to a 
partial polarization. 

It is the opinion of astronomers that some comets are 
self-luminous under certain circumstances, especially when 
they are near the sun. In receding from the sun, how- 
ever, they diminish in brightness more rapidly than they 
would if they shone by their own light only. 

According to a law of optics the brightness should vary 
inversely as the square of the distance the light has to 
travel to reach the eye. Now, in the case of a self-lumi- 
nous body the distance traveled by the light is equal to its 
distance from the earth, but in the case of a body shining 
by reflected solar light the distance traveled is equal to that 
from the sun to the body and thence to the earth. When 
a body of this class is moving directly away from both the 
sun and the earth, the distance traveled by reflected light 
increases twice as fast as its distance from the earth, and 
consequently the brilliancy of the body decreases four times 
as fast as it would if self-luminous. 



Distribution of Cometary Orbits. 

230. The orbits of about 250 comets have been com- 
puted with considerable accuracy. Of these, according to 
Young, 5 or 6 are hyperbolas, about 50 are ellipses, and the 
rest are parabolas. 

When the orbit is elliptical, the comet must return with 
due regularity ; but when it is either hyperbolical or para- 
bolical, the comet after passing its perihelion, will contin- 
ually recede from the sun, and ultimately must pass beyond 
the limits of his attraction, never to return. 

Observations can only be made on a comet when it is 
comparatively near its perihelion, and then from the nature 
of the case they must be more or less imperfect. Inasmuch 
as there is little difference in the shape of a parabola and a 



284 ASTROKOMY. 

very elongated ellipse in the neighborhood of their ver- 
tices, it may happen that many orbits which have been 
classed as parabolas are in reality elongated ellipses. 

When a comet passes near one of the large planets, its 
orbit is greatly disturbed, and often completely changed in 
form. This influence is manifested, to a certain extent, by 




Fig. 103. Projections of a few Cometary Orbits on the Plane of the Ecliptic. 

the grouping of those comets with which we are most 
familiar into classes, each of which corresponds to one of 
the large planets. Thus, the Jovian group contains 12 
comets whose periodic times range from 5 to 8 years, and 
whose aphelion points are tolerably near the orbit of Jupiter, 
some within and some without ; the Saturnian group con- 



COMETS AND METEORS. 285 

sists of 2 comets, with periods of from 12 to 15 years, and 
whose aphelia are at a distance from the sun nearly equal to 
the mean distance of Saturn ; the Uranian group contains 3 
comets with periods of about 33 years, and whose aphelion 
distances are nearly the same as that of Uranus ; the Nep- 
tunian group consists of 6 comets, whose periods range in 
the neighborhood of 75 years, and whose aphelion distances 
are all a little greater than the mean distance of Neptune. 
These groups embrace nearly one-half of all the comets 
whose orbits are certainly known to be elliptical. 

The order of grouping of a few of the periodic comets is 
shown in Fig. 103, in which their orbits are projected on 
the plane of the ecliptic. 

The orbits of comets are inclined to the ecliptic at almost 
every angle from 0° up to 90°, and their motions are about 
as likely to be retrograde as direct ; of a catalogue of 201 
comets given by Arago, 102 have a direct motion ; that is, 
they move from west to east, and 99 have a retrograde 
motion. From a comparison of a large number of orbits, 
Chambers reaches the following general conclusions : 

1°. " With comets revolving in elliptical orbits there is 
a strong and decided tendency to direct motion; the same 
obtains with the hyberbolic orbits ; with the parabolic 
orbits there is a rather large preponderance the other way ; 
and taking all the calculated orbits together, the numbers 
are too nearly equal to afford any indication of the exist- 
ence of a general law governing the direction of motion. 

2°. " There is a decided tendency in the periodic comets 
to revolve in orbits but little inclined to the ecliptic, and 
therefore a low inclination is an eminently favorable indica- 
tion of a periodic comet. 

3°. " There is a decided disposition in the orbits to con- 
gregate in and around planes inclined 50° to the ecliptic. 

4°. " There is an evident tendency in the perihelions to 
crowd together in two opposite regions, between 60°-120°, 
and 240°-300°," 



286 ASTRONOMY. 



Disintegration of Comets. 



231. Comets have sometimes been known to separate 
into two or more fragments. Grant, in his History of Phy- 
sical Astronomy, says: "Seneca relates that Ephorus, an 
ancient Greek author, makes mention of a comet which, 
before vanishing, was seen to divide itself into two distinct 
bodies. The Eoman philosopher appears to doubt the pos- 
sibility of such a fact ; but Kepler, with characteristic 
sagacity, has remarked that its actual occurrence is exceed- 
ingly probable. 

" The latter astronomer further remarked that there were 
some grounds for supposing that two comets, which ap- 
peared in the same region of the heavens in the year 1618, 
were fragments of a comet that had experienced a similar 
dissolution. Hevelius states that Oysatus perceived in the 
head of the great comet of 1618 unequivocal symptoms of 
a breaking up of the body into distinct fragments. The 
comet when first seen in the month of November appeared 
like a round mass of concentrated light. On the 8th of 
December it seemed to be divided into several parts. On 
the 20th of the same month it resembled a multitude of 
small stars. Hevelius states that he himself witnessed a 
similar appearance in the head of the comet of 1661." 

Biela's comet, having a period of about 6f years, and 
which was discovered in 1826, was seen in 1846 to separate 
into two distinct comets which continued to travel together 
at a distance of from 3' to 4' during the entire remaining 
period of their visibility. At this time the nuclei were 
separated by a distance of only 160,000 miles. 

On its return in 1852, the comet was still divided, but the 
component parts had separated to a distance of a million 
and a half of miles. It was not seen either in 1859, 
1865, or 1872. In the latter year, however, the earth 
passed through what was supposed to be the debris of the 



COMETS AND METEOKS. 287 

comet, and there is good reason to believe that the passage 
of some of its fragments through our atmosphere produced 
the meteoric shower of November 27th. This shower had 
been predicted, and the results verified the prediction. 

The great comet of 1882 showed many indications of dis- 
ruption, which were variously described by different as- 
tronomers. This comet passed its perihelion on the 17th of 
September. On the 4th of October the nucleus had become 
much elongated, and by the 10th of the same month it had 
taken on the appearance of an irregular string " of 6 or 8 
starlike knots of luminosity connected and veiled by shining 
haze." 

Prof. Young says, in speaking of this comet : " Another 
curious thing about the comet is the observation by Prof. 
.Schmidt of flocculent masses of light moving in the same 
direction as the comet; these were seen by Schmidt from 
October 8 to October 11, and were also observed by Barnard 
of Tennessee, and by Brooks of New York. These cloud- 
like masses were very faint, not visible to the naked eye, quite 
large, and they moved on in the same direction and finally 
disappeared. The probability is that they were debris of 
the comet's large tail following around and finally coming 
into the neighborhood of the comet itself." 

From these and other similar facts it has been thought 
by some that comets are frequently broken up into 
numerous fragments, which become scattered by disturbing 
forces both laterally and along the track of the comet, where 
they continue to revolve in the form of a stream of meteoric 
elements. 

Remarkable Comets. 

Halley's Comet. 

232. This comet is of special interest to astronomers, as 
it was the first one whose return had been predicted by 
means of mathematical computation. It appeared in 1682, 



288 ASTKONOMY. 

and Halley calculated, by Newton's method, the elements 
of its orbit. He found that the inclination of its orbit was 
17°42', the longitude of its perihelion 302°16', the longi- 
tude of its node 50°21', and its perihelion distance 54,000,000 
of miles, its motion being retrograde. 

He in like manner computed the elements of the comet 
of 1607, which he found to be almost identical with those 
given above. Again, by testing the observations made on 
the comet of 1531, he likewise found that its elements were 
also very nearly the same. He therefore inferred that the 
comets of those years were not different individuals, but so 
many reappearances of the same body, and he ventured to 
predict its return towards the end of 1758 or the beginning 
of 1759, allowing a few months for the changes in its orbit 
produced by the perturbations of the planets. 

Clairaut, a French astronomer, undertook the laborious 
calculations necessary to determine the changes that would 
be produced in its orbit by the perturbations of Jupiter 
and Saturn, and as the result of his investigations, he an- 
nounced that the comet would reappear within 30 days, one 
way or the other, of the middle of April, 1759. The comet 
actually passed its perihelion on the 13th of March, 1759, 
that is, about three days outside the limit assigned by the 
illustrious computer. This was, for these times, a wonder- 
ful triumph of science, particularly as the effects of pertur- 
bation were such as to cause a change of more than 600 
days in the comet's entire period. 

Damoiseau, with new elements, computed the time of its 
next return, and assigned November 4, 1835, as the date 
of its perihelion passage. Pontecoulant also made the com- 
putations and fixed upon November 13 as the time of its 
return to perihelion. In 1834, the path of the expected 
comet and its predicted positions for various dates from the 
20th of August to the 26th of December were published in 
the Annuaire du Bureau des Longitudes. True to predic- 
tion, the comet appeared on the 5th of August, followed 



COMETS AND METEORS. 289 

its assigned path, but a little behind time, and actually 
passed its perihelion on the 16th of November, only three 
days later than was predicted. 

The following table shows the dates of the comet's suc- 
cessive returns to perihelion for 500 years, from which we 
may infer the great changes produced by planetary pertur- 
bation : 

Perihelion passage. Time of revolution. 

1. Nov. 8, 1378. 

2. June 8, 1456 77 yrs. 212 days. 

3. Aug. 25, 1531. 75 yrs. 78 days. 

4. Oct. 26, 1607 76 yrs. 62 days. 

5. Sept. 14, 1682 74 yrs. 323 days. 

6. March 12, 1759 76 yrs. 189 days. 

7. Nov. 16, 1835 76 yrs. 249 days. 

From this table we see that the length of its time of 
revolution is greatly affected by perturbation ; the average 
time for six periods beiug 76 yrs. 62 days. 

Previous to the 2d of October, 1835, the comet presented 
a round nebulous disk with a faint nucleus at its centre. 
On the evening of that day the nucleus had become very 
bright, and according to Bessel a cone of light appeared to 
issue from the side next the sun, which, after extending for 
a short distance from the head, was observed to curl back- 
ward, as if impelled by a force of great intensity directed 
from the sun. This was the beginning of the formation of 
a tail. The nebulous matter, which in the first instance 
was repelled from the comet towards the sun, rising in the 
form of an envelope, was afterward repelled by a powerful 
force driving it away from the sun. 

The comet w T as observed by Sir John Herschel, after 
passing the perihelion. On the 25th of January it pre- 
sented no trace of a tail, but resembled a round nebulous 
body about 2' in diameter, surrounded by a coma of great 
extent. Within the disk was a small bright point, from 
13 



290 ASTROKOMY. 

which there issued in a direction opposite the sun, a ray of 
highly condensed light. The comet seemed to contain 
within it another miniature comet with a head and tail of 
its own. 

As the comet receded from the sun the head began to 
dilate and its light to grow fainter ; in consequence of 
successive additions to the length of its tail, the comet 
gradually assumed a paraboloidal form. The head aod 
paraboloidal envelope enlarged with great rapidity, and at 
the same time the comet diminished in brightness until it 
finally ceased to be visible for want of light. 

Donati's Comet. 

233. This comet was discovered by Donati at Florence 
June 2, 1858 ; it was then about 200 millions of miles from 
the sun, and at a still greater distance from the earth. By 
the 13th of June approximate elements had been determined 
and its future path predicted. By the middle of August its 
orbit had been determined with much accuracy. Traces of 
a tail became visible on the 20th of August, and on the 29th 
of that month the comet, which had hitherto been telescopic, 
became visible to the naked eye, and for several weeks there- 
after continued to be a conspicuous object in the northern 
heavens. 

It was observed in this country by Bond of Cambridge, 
who published an account of his observations in the Mathe- 
matical Monthly, from which article we gather some of the 
more important facts of its history. 

Bond says that the nucleus had a diameter of about 2000 
miles on the 8th of September, with a surrounding nebu- 
losity of about 3000 miles in diameter, while a diffused light 
extended for 40,000 or 50,000 miles toward the sun. At 
this time its tail was about 16 millions of miles in length. 
On the 20th of that month the train or tail was plainly 
bifurcated, the nebulous matter issuing from the head in two 



COMETS AND METEORS. 291 

streams, of which the southern one was the brighter; its 
general outline was in the shape of an elongated hyperbola 
or parabola. By the 23d of September the nucleus had be- 
come as bright as a large star of the first magnitude, and it 
was about this time that Bond began to notice the forma- 
tion of successive envelopes, which became so marked a 
feature in the history of this comet ; its tail at this period 
was about 6° or 8° long, even in the presence of bright 
moonlight. In the telescope the nucleus appeared to 
be diminished in diameter, and its light was very intense ; 
outside of this, and about 6,400 miles distant, was a bright 
envelope, and still outside of this was a fainter envelope ; 
the tail was slightly curved. 

By the 25th a new envelope was thrown off, which be- 
came clearly visible on the 27th, and as it expanded the 
tail received a new appendage in the shape of a ray of light 
nearly straight, and apparently tangent to the curved part 
of the tail, as shown in Fig. 101. On the 29th the comet 
was 50 millions of miles from the sun and 70 millions of 
miles from the earth, and its tail had become 26 millions of 
miles in length. At this time the nebulous matter was be- 
ing thrown off with commotion, the jets streaming forth in 
various directions, but blending together and becoming more 
symmetrical as the matter rose from the comet. 

The comet passed its perihelion on the 29th of Sep- 
tember, and was nearest the earth on the 10th of October. 
Its rapid passage to the southern hemisphere rendered it 
invisible in the northern hemisphere after the end of Octo- 
ber, though it was seen in the southern hemisphere as late 
as March 4, 1859. 

After its perihelion passage new envelopes continued to 
be thrown off, and the nucleus continued to diminish in 
size. When at its brightest five distinct envelopes could 
be seen at the same time, separated from each other 
by dark bands. Rays or jets of luminous matter were 
numerous, each shooting forth from the convex side of 



292 ASTRONOMY. 

the tail, which at its maximum was about 57,000,000 of 
miles in length. 

At this time the comet's appearance, as drawn by Bond, 
is shown in Fig. 101. 

In many respects this is the most remarkable comet that 
has been seen in modern times, and furthermore, it was 
more carefully studied than any previous comet. 

Its orbit was computed by various astronomers, but the 
results of their labors were somewhat discordant: the 
periodic time was variously assigned from 1,620 up to 2,470 
years ; from this discrepancy we may infer the great diffi- 
culty of the problem of determining the exact orbit of such 
a comet. 

Comparison of Halley's and Donati's Comets. 

234. Phenomena similar to those just described were 
noticed at the last appearance of Halley's comet. The con- 
clusions deduced by Sir John Herschel are apparently con- 
firmed and strengthened by the observations made on 
Donati's comet. These conclusions, as summarized by 
Herschel in his- Outlines of Astronomy, are as follows: 

1°. That the matter of the nucleus is powerfully excited 
and dilated into a vaporous state by the sun's rays, escaping 
in streams and jets at those points of its surface which op- 
pose least resistance, and in all probability throwing the 
nucleus into irregular motions in the act of escaping, thus 
altering its direction. 

2°. That this process takes place in that portion of the 
nucleus which is turned toward the sun, the vapor escaping 
chiefly in that direction. 

3°. That when so emitted it is prevented from proceed- 
ing in the direction of the force of emission by some force 
directed from the sun, which drifts it back and carries it 
out to a vast distance behind the nucleus/ forming the tail, 
or so much of the tail as can be considered as consisting of 
material substance. 



COMETS AND METEORS. 293 

4°. That the force, whatever may be its nature, acts un- 
equally on the materials of the comet, the greater portion 
of which remains un vaporized, a considerable part of the 
vapor actually produced remaining in the neighborhood to 
form the coma. 

5°. That the force thus acting on the material of the tail 
cannot possibly be identical with gravitation, being cen- 
trifugal, or repulsive with respect to the sun, and of an 
energy far exceeding the gravitating force toward that body. 

6°. That unless the matter of the tail thus repelled from 
the sun be retained by a peculiar and highly energetic at- 
traction toward the nucleus, differing from and exceptional 
to gravitation, it must leave the nucleus altogether ; it is 
therefore conceivable that a comet may lose at each approach 
to the sun a portion of that peculiar matter, whatever it may 
be, on which the production of the tail depends, the remain- 
der being of course less excitable by solar action and more 
impassive to his rays, and therefore more nearly approxi- 
mating to the nature of the matter of planetary bodies. 

7°. That considering the immense distances to which 
some of the matter of the tail is carried from the comet, it is 
quite inconceivable that the whole of that matter should 
be reabsorbed, and therefore that it must lose during 
its perihelion passage some portion of its matter; and 
if, as would seem far from improbable, that matter should 
be of a nature to be repelled from, not attracted by, 
the sun, the remainder will by consequence be more ener- 
getically attracted to the sun than the mean of both. If, 
then, the orbit be elliptic, it will perform each revolution in 
a shorter time than the preceding one, until at length the 
whole of the repulsive matter will be thrown off. 

The Great Comet of 1882. 

235. This comet was first seen and observed in the 
southern hemisphere on the 7th or 8th of September, 1882. 



294 ASTKONOMY. 

On the 17th, the day of its perihelion passage, it was ob- 
served at the Cape of Good Hope in broad daylight, and 
when in the immediate neighborhood of the sun. Mr. Gill 
says: " The comet was followed by two observers with sep- 
arate instruments right up to the sun's limb, when it sud- 
denly disappeared at 4h. 50m. 58s. mean local time." After 
passing to the west of the sun it continued visible by day- 
light for a day or two, and was seen by various astronomers 
in all parts of the world. A few days after its perihelion 
passage it became a . conspicuous object in the eastern 
heavens before daylight, and continued visible, with dimin- 
ishing brightness, for several weeks. 

In passing its perihelion, which it did at a distance of 
only 300,000 miles from the sun's surface, its orbital velo- 
city was so great that it moved through an angle of 180° in 
less than 4 hours ; it must have passed through the sun's 
coronal atmosphere at the rate of about 300 miles per 
second. 

On the 2d of October its nucleus was as bright as a large 
star of the Jirst magnitude, and the coma and tail were well 
developed, with a clearly marked dark streak extending 
backward from the nucleus. It was noticed at this time 
that the nucleus, instead of being round, was elongated in 
the direction of the comet's radius-vector ; it continued to 
elongate, and in about a week it presented the appearance 
of a string of knotted star-like points. Its tail was very 
broad and bright, with a slight curvature ; its length on 
the 15th of October was about 60 millions of miles, which 
corresponded to an arc of 18° of the heavens. 

The spectroscopic observations of Thollon and others 
indicated the presence of incandescent sodium in the nu- 
cleus ; the nucleus also gave a nearly continuous spectrum 
in which the Frauenhofer dark lines were quite inconspicu- 
ous, showing that but little of the comet's brilliancy was 
due to reflected solar light. Eicco of Palermo saw, besides 
the bright sodium line, several other bright lines, but for 



COMETS AND METEORS. 295 

want of suitable means was unable to locate their position 
in the spectrum. 

When the elements of this comet were compared with 
those of preceding comets, they were found to bear a strik- 
ing resemblance to those of the comets of 1880, of 1843, 
and of 16G8. From the computed lengths of the periods of 
these comets, it seemed almost impossible to believe that it 
could be a return of any one of them ; we are therefore led 
to the conclusion that it is one of a group or family which 
are revolving in nearly the same orbit. This conclusion 
will not appear improbable when we come to consider the 
relation between comets and meteor streams. 

Prof. Young, in writing on this comet, notices a phe- 
nomenon somewhat similar to that already spoken of as 
having been seen in connection with Halley's comet. He 
says that iRicco's drawing of the comet as it appeared on 
the 4th of October shows something resembling a bright 
comet enveloped in a fainter one. He further says : " Prof. 
Smith of Kansas University noticed on the 9th a pale 
stream of light with parallel edges, and nearly as wide as 
the tail of the comet, extending towards the sun. On the 
15th this phenomenon had become much more conspicuous. 
The streamer was now one-half a degree in width, well 
defined at both edges, of nearly uniform brightness through- 
out, though nowhere as bright as even the faintest portion 
of the tail, and extended from its origin, a degree or two 
above the nucleus, to a distance of two or three degrees 
below the head, where it faded out." 

The comet remained visible in the telescope till May ; 
it was observed on the 6th of April by Eicco, at which time 
it was about 5 hours west of the sun. 

Encke's Comet. 

236. This comet, which was first noticed by Pons of 
Marseilles, derives its name from the astronomer who first 



296 ASTRONOMY. 

computed its orbit. From the observations made in the 
latter part of 1818 and the beginning of 1819, Encke found 
that the comet revolved around the sun in an elliptical 
orbit in the short period of about 3^ years. 

In comparing the elements of this comet with those of 
the comets that were visible in 1795 and 1805, he con- 
cluded that they were identical, and he also inferred that 
it would return in 1822 ; but at the date assigned its posi- 
tion in the heavens was such as to prevent its being seen 
in the northern hemisphere, but it was seen and observed 
by M. Biimker of Paramatta for about three weeks. The 
observations thus obtained enabled Encke to predict its 
next return, which he found would occur on the 16th of 
September, 1825. 

It was seen at this return, and also to better advantage 
on its return in 1828. On the 30th of November, or more 
than a month before its perihelion passage, it was visible to 
the naked eye as a star of the 6th magnitude, and a week 
later it appeared as a star of the 5th magnitude. In 
the telescope it appeared to be a slightly oval mass of 
nebulous matter with a nucleus excentrically situated on 
the side nearest the sun. 

This comet is rendered remarkable by the continued 
diminution of its periodic time, which amounts to about 2J 
hours at each successive return. This peculiarity had been 
noticed by Encke, who suggested that space was filled with 
a rare ethereal medium, sufficiently dense to produce by its 
resistance an effect on the motion of the comet, but of such 
tenuity as to exercise no sensible effect on the motions of 
the more massive planets. 

" The contraction of the orbit must be continually pro- 
gressing, if we suppose the existence of such a medium, and 
we are naturally led to enquire, what will be the final con- 
sequence of this resistance. Though the final catastrophe 
may be retarded for many ages by the powerful attraction 
of the larger planets, especially Jupiter, will not the comet 



COMETS AND METEORS. 297 

be at last precipitated on the sun ? The question is full of 
interest, though altogether open to conjecture." 

The rate of diminution is shown in a table constructed 
by Encke, and which may be found in Chambers' Astron- 
omy. From this table we see that the diminution has pro- 
gressed with great regularity ; in 1795 the periodic time was 
1212.55d., in 1822 it was 1211.66d., in 1852 it was 1210. 65d., 
and in 1865 it was reduced to 1210. 22d. 

It would seem, if the retardation spoken of, and which 
acts to diminish the periodic time, is due to a resisting 
medium, that it would produce similar effects on other 
comets ; but no such effect has been shown. The question 
of the existence of a resisting medium is, and must remain, 
unsettled until further investigations have been made. 

Meteorites. 

237. Besides the bodies already described as members of 
our system, there are undoubtedly multitudes of cosmical 
bodies which are embraced within the limits of the sun's 
attraction, but which on account of their minute size must 
remain forever invisible and unknown to us, except when 
they come so near the earth as to be involved in her at- 
mosphere ; then, in accordance with well-known physical 
laws, they become heated to such an extent as to make 
them luminous and consequently visible. These bodies will 
be considered under the general name of meteorites ; as 
we shall see hereafter, these bodies, as well as the planets, 
are subject to the law of universal gravitation ; they also 
possess all the attributes of terrestrial matter, and like it are 
subject to the same physical laws. 

When a very small meteorite enters our atmosphere it 
becomes incandescent and is visible for a short time, as it 
moves along its path, constituting what is called a shoot- 
ing star. When the meteorite is larger and when it be- 
comes involved in a denser portion of the atmosphere, it 



298 ASTRONOMY. 

presents the appearance of a brilliant planet; it is fre- 
quently followed by a train of greater or less extent, and 
oftentimes it explodes with more or less violence ; it is then 
called a fire-ball. When the meteorite is still larger it fre- 
quently escapes destruction in the atmosphere and falls to 
the earth, either as a unit, or, after one or more explosions, 
in fragmentary portions ; the masses that reach the earth 
are called aerolites. All these phenomena are styled 
meteoric, and it is probable that they are all essentially 
identical. 

Shooting Stars. 

238. The phenomenon of a shooting star is by no means 
a rare one. It is within the experience of every one who 
has watched the heavens for a single hour that shooting 
stars are of constant occurrence. 

Ordinarily a bright point of light, resembling a star, 
shoots along the sky for a certain distance and then disap- 
pears from view. Sometimes it leaves a faint train behind 
it which continues visible for a short time after the stellar 
pointy or nucleus, has disappeared, much as a rocket marks 
its course by the train of light which it leaves along its 
path. Shooting stars of this kind can be seen every fair 
evening, and usually as many as four or five are visible 
every hour. At certain times they are so numerous as to 
constitute what is called a meteoric shower. 

Meteoric Showers. 

239. Many meteoric showers have been noticed, the most 
striking of which are of periodical occurrence. Among the 
most remarkable of these periodic showers is that which 
takes place about the 13th of November, and that which 
happens about the 10th or 11th of August. The November 
meteors are most numerous at intervals of 33 or 34 years ; 
the August meteors are visible every year ; the reasons of 



COMETS AND METEORS. 299 

these variations will be apparent when we come to explain 
the theory of their occurrence. 

Ordinary shooting stars are believed to be due to individ^ 
ual meteorites; meteoric showers are accounted for by sup- 
• posing that innumerable streams of meteorites are re- 
volving around the sun in regular orbits, and subject, like 
other bodies of the solar system, to planetary perturbation. 
These streams are often of enormous breadth, perhaps mil- 
lions of miles, and the meteorite masses are supposed to be 
distributed along them, either uniformly, or in condensed 
groups. It is further supposed that the earth's orbit inter- 
sects some of these streams, and that meteoric showers oc- 
cur when the earth is passing these points of intersection. 

When the earth passes through a part of the stream where 
the meteorites are sparsely distributed, the corresponding 
shower is inconspicuous ; but when it passes through the 
denser regions of the stream, the meteoric display is exceed- 
ingly brilliant. 

It is undoubtedly the case that there are multitudes of 
these streams which are not intersected by the earth's orbit, 
as w r ell as others which are just grazed by it, or through 
which it passes excentrically. 

The cause of a meteor's becoming luminous is easily 
explained. Whenever a meteorite enters the Earth's atmos- 
phere, which it usually does with planetary velocity, it 
experiences a resistance, whether by friction or by collision 
with the aerial particles, by virtue of which its velocity is 
diminished ; and in accordance with a law of physics a por- 
tion of the body's energy of motion is converted into heat, 
which soon renders the body incandescent. 

The varied circumstances of size, velocity, and direction 
of motion serve to explain all the irregularities of appear- 
ance presented by these remarkable bodies. There is good 
reason to believe that a great majority of them are very 
small, in fact mere particles of cosmical dust ; these are 
totally consumed in their transit through the atmosphere. 



300 ASTRONOMY. 

Some are larger, and they may be either consumed in the 
atmosphere, or they may escape total destruction and con- 
tinue their motion through space ; others again may enter 
our atmosphere in such a direction that their relative 
velocity with respect to the earth is comparatively small, • 
and these may fall to the earth with little or no physical 
change. 



November Meteors and Tempel's Comet. 

240. A remarkable shower of meteors took place on the 
13th of November, 1799. It was visible over the greater 
part of North and South America, having been witnessed 
by the Moravian missionaries in Greenland, and by Hum- 
boldt, who was then traveling in South America. 

In Humboldt's description of the phenomenon, he says : 
"Towards the morning of the 13th we witnessed a most 
extraordinary scene of shooting meteors. Thousands of 
bodies and falling stars succeeded each other for four hours. 
Their direction was very regular from north to south. 
From the beginning of the phenomenon there w T as not a 
space in the firmament equal in extent to 3 diameters of 
the moon which was not filled every instant with bodies or 
falling stars. All the meteors left luminous traces or phos- 
phorescent bands behind them, which lasted seven or eight 
seconds." 

Mr. Ellicott, who witnessed the display from a vessel in 
the Gulf of Mexico, says: "The phenomenon was grand 
and awful. The whole heavens appeared as if illuminated 
with sky-rockets, which disappeared only with the light of 
the sun, after daybreak. The meteors, which at any one 
instant of time appeared as numerous as the stars, flew in 
all possible directions, except from the earth, towards which 
they were all inclined, more or less ; and some of them 
descended perpendicularly over the vessel we were in, so 
that I was in constant expectation of their falling on us." 



COMETS AND METEORS. 301 

Meteoric showers took place on the 13th of November, 
in 1831 and 1832, but the most interesting display was on 
the 13th of November, 1833. It was, like the shower of 
1799, visible over a large part of America, especially in the 
United States, where it commenced about midnight and 
continued till morning. 

Its character was similar to that described by Humboldt ; 
its effect on the minds of the negroes is thus described 
by a Southern planter : " I was suddenly awakened by the 
most distressing cries that ever fell on my ears. Shrieks of 
horror and cries for mercy I could hear from most of the 
negroes of three plantations, amounting in all to about 600 
or 800. While earnestly listening for the cause, I heard a 
faint voice near ' my door calling my name. I arose, and 
taking my sword, stood at the door. At this moment I 
heard the same voice still beseeching me to rise, and saying 
1 Oh, my God, the world is on fire ! ' I then opened the 
door, and it is difficult to say which excited me most, the 
awfulness of the scene or the cries of the distressed negroes. 
Upwards of one hundred lay prostrate on the ground, some 
speechless, and some with the bitterest cries, with their 
hands raised, imploring God to save the world and them. 
The scene was truly awful, for never did rain fall much 
thicker than the meteors towards the earth ; east, west, 
north, and south, it was the same." 

From about 2 o'clock for a period of two or two and a 
half hours the number of meteors which fell was too great 
for computation. They were of all sizes, from mere phos- 
phorescent points up to the most magnificent fire-balls. It 
was found, by tracing back their luminous paths, that they 
all seemed to emanate from the neighborhood of the star 
y Leonis, and this without reference to its altitude. The 
various reports of this meteoric display were collated by Prof. 
Olmstead of New Haven, and by Prof. Newton, who was led 
to examine the previous records of similar showers. Abun- 
dant evidence was found to establish the belief that the 



302 ASTRONOMY. 

November meteor showers were of a periodic character, and 
a return of the phenomenon was predicted in 1866. At this 
time, the heavens were carefully watched by many observers 
on both continents. 

The number of meteors seen in America was not as great 
as had been expected, but the display in Europe, though 
not so grand as those that have been described, was ex- 
ceedingly striking. It was estimated that 10,000 meteors 
were observed at Greenwich, all of which seemed to radiate 
from a point between y and e Leonis. Mr. Dawes, who 
observed the phenomenon, says that 2,800 meteors were 
counted by himself and one assistant looking toward 
the east in the course of 2} hours, while another as- 
sistant looking west counted about 400 an hour until he 
became bewildered by six or seven bursting out simulta- 
neously. 

From all the data that can be gathered it appears that 
the great November showers occur at intervals of 33 or 34 
years, but that minor showers take place on the 13th of 
November for a few years both before and after the 
maximum displays. From these facts it is inferred that the 
November meteors are due to a ring or stream of meteorites 
circulating around the sun, through which the earth passes 
on or about the 13th of November each year ; the extraor- 
dinary showers are supposed to correspond to the passage 
of the earth through a part of the stream where the meteor- 
ites are densely packed, and which is believed to be some 40 
or 50 millions of miles in length ; in ordinary years the 
path of the earth is through portions where the meteorites 
are fewer in number. 

The orbit of this stream of meteorites has been computed 
with considerable accuracy, and it is found to be very 
nearly the same as that of Temple's comet, which passed 
its perihelion in January, 1866, as will be seen from the 
following table : 



COMETS AND METEORS. 303 

Meteors. Comets. 

Longitude of perihelion 56°26' 60°28' 

Longitude of ascending node 231°28' 231°26' 

Inclination to ecliptic 17°45' 17°18' 

Excentricity 0.9046 0.9054 

Perihelion distance 0. 9873 0.9765 

Period 32.25y. 32.18y. 

Motion retrograde retrograde. 

Its aphelion distance is somewhat greater than the dis- 
tance of Uranus, so that this meteoric stream and its ac- 
companying comet belong to the Uranian group. 

The fact of the comet's orbit coinciding so nearly with 
that of the meteoric stream seems to indicate a connection 
of some kind: whether the comet consists of a compacted 
mass of the meteorites constituting the stream, or whether 
the meteorites have resulted from the disintegration of a 
comet which was once far larger than Tempel's comet, is 
perhaps undecided. 

The August Meteors and the Third Comet of 1862. 

241. The August meteors are less striking than those of 
November, but they are more regular in their appearance. 
Every year from the 9th to the 12th of August an un- 
usual number of meteors may be seen, whose paths on 
being traced back are found to intersect at a point in the 
constellation Perseus. This point, which is called the ra- 
diant point, has caused the August meteors to be called 
Perseids, and for a similar reason the November meteors, 
which radiate from a point in Leo, are called Leonids. 

It is inferred that the August meteors are due to a stream 
of meteorites of enormous extent through which the earth 
passes about the 10th or 11th of August ; it is also believed 
that the meteorites which constitute this stream are more 
equably distributed than in the November stream. 



304 



ASTRONOMY. 




Fig. 



104. Orbit of the August 
meteors. 



The orbit and the extent of 
this stream, which is shown in 
Fig. 104, were investigated by 
Schiaparelli, who found that in 
some of its elements it was 
closely analogous to the third 
comet of 1862, sometimes called 
Tuttle's comet. The extent of 
this resemblance is shown in the 
following table of elements : 

Tuttle's August 

comet, meteors. 

Longitude of perihelion 344 °40' 343°38' 

Longitude of ascending node 138°15' 137°27' 

Incline to ecliptic 66°25' 63' 8' 

Perihelion distance 9626 .9643 



The excentricity of the me- 
teoric orbit is such as to throw 
its aphelion point beyond the 
orbit of Neptune, so that this 
group of meteorites, and perhaps 
also Tuttle's comet, belong to 
what we have already spoken of 
as the Neptunian group of 
comets. 

It is believed that other mete- 
oric streams are, in like manner, 
closely related to corresponding 
comets. 



Heights at which Shooting Stars are Seen. 

242. The most systematic attempt to ascertain the 
height above the earth at which a shooting star may be 



COMETS AKD METEORS. 305 

seen was that made by the officers of the U. S. Naval Ob- 
servatory on the occasion of the November shower in 1867, 
and which is alluded to by Prof. Newcomb in his Popular 
Astronomy. 

He says that Prof. Harkness was sent to Richmond to 
map the apparent paths of the brighter meteors there visi- 
ble, which were afterwards compared with their apparent 
paths as seen from Washington. Prof. Newcomb says : 
"The general result was that they were first seen at an 
average height of 75 miles, and disappeared at a height of 
55 miles. There was no positive evidence that any meteor 
commenced at a height much greater than 100 miles." 

Motions of Shooting Stars Described. 

243. Some shooting stars move so rapidly that the eye 
can scarcely follow them, whilst others remain visible for a 
considerable fraction of a minute, moving so slowly that 
their path can easily be traced out amongst the stars. Some 
move at the rate of 40 to 50 miles a second, whilst others 
travel no more than one-fourth or one-fifth as fast. 

Some describe arcs of but a few degrees in extent, others 
are visible through more than 90° of arc. Some are so 
small as to be almost evanescent, others are more brilliant 
than the brightest star or planet. 

It is to be noted that meteors, as a general. rule, and this 
is especially the case with these constituting a meteoric 
shower, are more numerous after midnight than before. 
This fact is explained by the circumstance that we are at 
that time on the hemisphere of the earth which is turned 
toward the direction in which the earth is moving in its 
journey around the sun. 

Fire-balls. 

244. Fire-balls, as already intimated, are similar to shoot- 
ing stars, only much larger. They often appear to be nearly 



306 ASTRONOMY. 

as large as the moon, with long and brilliant trains, and 
sometimes they appear to burst like a rocket. Not infre- 
quently they are so bright as to be seen in broad daylight. 
Arago gives a list of more than 650 fire-balls, of which 
nearly half have appeared during the present century. 

The following quotation from his list shows some of the 
leading characteristics of this peculiar species of meteor : 
"1836, February 12, at 6h. 27m. in the morning, a fire-ball 
was seen at Cherbourg moving from the east. Its appear- 
ance was that of a ball of fire, and to the naked eye it 
seemed to have a disk nearly equal to that of the full moon. 

"It was of a purplish color, and its light was intense 
enough to illumine the entire horizon, so that people could 
read in the streets as though it were broad day. It was sur- 
rounded by a whitish envelope, which was obscured at a sin- 
gle point by vapor emitted from the ball. It seemed to be 
no more«than 900 feet above the hills over which it passed. 
On its first appearance it moved at the rate of half a league 
per minute with a well-marked rotation on an axis. 

"It seemed to stop for a time, and then moved on with 
the speed of an arrow, falling to the earth at the distance 
of 12 leagues with an explosion similar to that of a salvo of 
artillery. It had a train of a whitish color that narrowed 
down to a point." 

Chambers quotes the following description of a fire-ball 
seen by Kev. T. W. Webb in Herefordshire, England, on 
the 12th of November, 1861: "About 5h. 45m. . . . we 
were walking, a party of three persons, along a wide turn- 
pike road, fully lighted by a moon 10 days old, when we 
were surrounded and startled by an instantaneous illumina- 
tion, not like lightning, but rather resembling the effect of 
moonlight suddenly coming out from behind a dark cloud 
in a windy night ; it faded very speedily, but on looking 
up we all perceived at a considerable altitude, perhaps 60° 
or 70°, a superb mass of fire, sweeping onward and falling 
slowly in a curved path down the southwestern sky. 



COMETS AXD METEORS. 307 

"Its form was that of a pear, or more precisely an in- 
verted balloon, and its size probably 30' by 15' at first, if 
not more ; but it gradually diminished, and by the time it 
had attained the middle of its course it may not have ex- 
ceeded 20' by 10'. Its light was a beautiful blue, resem- 
bling, though far surpassing in vivid intensity, the hue of 
the asteroid Flora as we saw it many years ago with the 
7-inch object-glass of the telescope now at the Greenwich 
Naval School. 

"Kuddy sparks, of the color of glowing coals, were left 
behind at its smaller end, and its path was marked by a 
long pale streak of little permanency. . . . The whole 
duration may have been as much as 5 seconds. Its aspect 
was decidedly that of a liquefied and inflamed mass, and the 
immediate impression was that of rapid descent ; but as its 
apparent magnitude diminished so much, it is not improba- 
ble that it was in reality moving in a course not greatly 
inclined to the surface of the earth." 

Humboldt, after saying that smoking luminous fire-balls 
are sometimes seen, even in the brightness of tropical day- 
light, equaling in size the diameter of the moon, gives the 
following fact : "A friend of mine was in the year 1788 at 
Popayan, a city which is in 2° 26' 1ST. lat. and at an eleva- 
tion of 5,583 ft. above the sea, and at noon when the sun 
was shining brightly in a cloudless sky, saw his room 
lighted up by a fire-ball. He had his back turned to the 
window at the time, and on turning around perceived that 
a great part of its path was still illuminated by the brightest 
radiance." 

In the month of July, 1860, a remarkable fire-ball passed 
over the State of New York and part of New England in 
the early eveuing, which was seen by thousands of people. 

It entered the United States near Niagara Falls, and 
moving a little south of east crossed the entire State of 
New York, leaving it in the neighborhood of Yonkers; it 
was seen passing over the southwestern part of Connecticut 



308 ASTRONOMY. 

and across Long Island Sound, and was finally seen at sea 
nearly 400 miles east of Montauk Point. 

To the observers along its path it seemed on the point of 
falling to the earth, but it is believed that it escaped de- 
struction, and after passing through our atmosphere con- 
tinued its path through space. This body was of enormous 
size, some observers of good judgment estimating its actual 
diameter to be as great as half a mile. 



Aerolites. „ 

245. In most cases the material substances constituting 
shooting stars are so far consumed that no part reaches the 
earth, unless it be in the form of an impalpable powder or 
dust. Occasionally, however, solid metallic or mineral 
masses fall to the earth, giving us an opportunity to study 
the physical constitution of these extra-terrestrial masses 
of cosmical matter. 

The chemical elements of which aerolites are composed 
are the same as are found in terrestrial bodies ; some of the 
most important of these are iron, nickel, cobalt, manganese, 
chromium, copper, arsenic, zinc, potassium, sodium, sul- 
phur, phosphorus, and carbon. The manner in which these 
elements are combined is in some cases such as to give a 
somewhat peculiar feature to the mineral compounds which 
are found in these bodies, and it is frequently the case that 
the forms of crystalline aggregation which they offer are 
different from our terrestrial minerals. These peculiarities 
have enabled scientists to identify many mineral masses that 
have been found, from time to time, as belonging to the 
class of meteorites. 

The crystalline structure of some of the aerolites is 
shown in Fig. 105. 

In many specimens the principal elements are iron and 
nickel ; in seme cases the amount of iron is no less than 96 
per cent, of the entire mass ; they are also frequently richer 



COMETS AND METEORS. 



309 



in nickel than our finest nickel ores. In other specimens 
the elements are principally of an earthy character, scarcely 
2 per cent, of iron being present. Some are largely com- 
posed of phosphorus, iron, and nickel, and some of com- 
pounds of sulphur and magnetic pyrites. But in no case 
has any element been discovered that is not recognized as a 
•terrestrial substance. 




Fig. 105. Copy of a Print. 



Explanation. Fig. 105 is a copy of a print made by using a section of an 
aerolite which had been acted upon by an acid. 



As an illustration of the composition of the ferruginous 
class of aerolites, we may cite the case of a meteoric body 
that was found by Gen. Carlton, of the IT. S. Army, in 
Arizona. This body was found in 1864, and is now in pos- 
session of the kSociety of Pioneers of San Francisco. It is over 
4 feet in length, and it weighs 632 lbs.; at the time of its 
discovery it was used by the Indians as a sort of anvil, 
on which they hammered out their rude copper implements. 
A portion of this aerolite has been analyzed by Prof. Brush 
of Yale College, with the following result: 



310 ASTRONOMY. 

Per cent 

Iron 81.56 

Kickel 9.17 

Cobalt 0.44 

Copper 0.08 

Phosphorus 0.49 

Silica 3.63 

Protoxide of Iron 0.12 

Lime 1.10 

Magnesia 2.43 

99.02 
with traces of alumina, chlorine, sulphur, and chromium. 
Most aerolites when found are coated by a thin crust of 
fused material, which has a glossy, pitch-like appearance ; 
this crust is indicative of the sudden and intense heat to 
which they have been exposed in their transit through our 
atmosphere. The crust is usually separated from the in- 
terior mass by a well-marked surface, and as a general thing 
the interior nucleus bears no trace of fusion. 

Size of Aerolites. 

246. The sizes of aerolites vary from the minutest par- 
ticles up to masses weighing hundreds of pounds. An 
immense one was discovered in Siberia weighing 1,680 lbs., 
which now forms an attractive feature in the Imperial 
Museum of St. Petersburgh. A specimen weighing about 
1,400 lbs. was found in Brazil and sent to England, being 
at present in the British Museum; this is supposed to be 
only a fragment of an enormous body, of which a still 
larger portion has never been removed. The great aerolite 
found in Arizona, and already referred to, weighs more 
than 600 lbs. 

The aerolites above mentioned were not seen to fall, but 
are known to belong to this class of bodies by their physical 
characteristics. Besides these and numbers of others of like 



COMETS AND METEOKS 311 

character, there are multitudes scarcely less in magnitude 
which have been seen to strike the earth. 

Arago gives a catalogue of 237 which have fallen since 
the beginning of the Christian era, most of which belong to 
modern times. Of these we may mention an aerolite which 
fell at Vouille in 1831, and which weighed 45 lbs.; one fell 
at Ohantourney in 1812, weighing 76 lbs.; one at Juvenas 
in 1821, whose weight was 207 lbs., and one in New 
Grenada in 1810, which weighed 1,688 lbs. The last was 
composed of 92 parts of iron and 8 parts of nickel ; it had 
no external crust and was only a fragment. 

The fall of these bodies has not been unattended with 
danger to property and to life. A stone is said to have 
fallen in China in the year 606, which killed ten men and 
did other damage. In 1764 an aerolite fell on the deck of a 
ship in the Dutch East India service, which killed two 
sailors. About the same time one fell in Milan, killing a 
Franciscan monk. 

The chemist Laugier left in his cabinet a splinter of an 
aerolite which was said to have fallen in Rockford (in the 
United States) ; this stone killed a farmer, destroyed a cot- 
tage, and was buried six feet in the earth. On the 7th of 
March, 1618, the Palais de Justice, in Paris, was burned, 
supposed to have been set on fire by a falling meteor; and 
in 1761 a house was burned at Chambleau, having been set 
on fire in like manner. Many other instances of accidents 
from these bodies have been recorded. 

Remarkable falls of Aerolites. 

247. The following instances of remarkable falls of aero- 
lites are taken from Prof. Kirkwood's valuable work on 
Comets and Meteors : 

In 1795 a large meteoric stone fell in Yorkshire, Eng- 
land. Several persons heard the report of an explosion in 
the air, followed by a hissing sound, and afterward felt a 



312 ASTRONOMY. 

shock as of a heavy body falling to the ground. A plow- 
man saw a stone fall, throwing up the mould on every side. 
It penetrated the soil, lodging in the chalk rock below. 
When raised it was found to weigh 56 lbs. The noise of 
the explosion was heard over a considerable district. 

A fall of aerolites happened at L'Aigle, France, on the 
26th of April, 1803. At 1 o'clock a tremendous noise was 
heard, and at the same time an immense fire-ball was seen 
moving through the atmosphere with great rapidity. A 
violent explosion followed, which was heard for seventy 
miles around. A great number of meteoric stones fell to 
the earth, of which about 3,000 were picked up; the largest 
of them weighed 17 pounds. 

Early in the present century a large meteor exploded over 
Weston, Connecticut, just after daybreak. Its apparent 
diameter was half that of the full moon, and its time of 
flight was about 30 seconds. Within less than a minute 
from the time of its disappearance three distinct reports 
like discharges of artillery were heard, and each explosion 
was followed by a fall of stony fragments, which when first 
found were so soft as to be easily pulverized between the 
fingers. 

On the 1st of May, 1860, a shower of meteoric stones fell 
in Guernsey county, Ohio. The meteor passed over at 1 
o'clock, P.M., and was disrupted by a succession of explo- 
sions. As a result, a shower of stony fragments fell over 
an area of about ten miles in length and three miles in 
width. The largest piece picked up weighed 103 lbs. ; it 
struck the earth at the foot of an oak tree, and after cut- 
ting off two roots, one five inches in diameter, and grazing 
a third, it penetrated a bed of hard clay to a depth of two 
feet and ten inches. 



XII. THE SUN AND THE STARS. 

The Sun's Rank among the Stars. 

248. The sun is one among a vast host of similar bodies 
that we have called fixed stars, and it is not supposed that 
he differs in any material respect from the other individuals 
of his class. 

It is believed with good reason that he is neither one of 
the largest nor one of the smallest of these bodies ; so that 
if he were removed to a distance from us equal to that of 
the other stars he would appear no brighter than they. 

If he were placed at a distance from us equal to that of 
the nearest star, he would subtend an angle of less than a 
hundredth part of a second of arc, that is, he would appear 
no larger than would a globe one foot in diameter at a dis- 
tance of 4,000 miles ; hence, his disk would have no appre- 
ciable diameter even in the most powerful of our telescopes. 

Apparent Proper Motions of the Stars. 

249. As stated in Art. 42, many of the stars have proper 
motions sufficiently great to admit of measurement. This 
fact was suspected as early as 1717 by Halley, who com- 
pared the places of the three prominent stars, Sirius, 
Arcturus, and Aldebaran, as determined by the observa- 
tions of the early Alexandrian astronomers, with their 
known positions at the time of making the comparison. 

After making due allowance for changes in the positions 
of the vernal equinox and the equinoctial, the result indi- 
cated that these stars had moved in the interval through 
arcs of 37', 42', and 33', respectively. Inasmuch as the 
14 



314 ASTRONOMY. 

ancient observations must have been very defective, but 
little reliance could be placed on the corresponding rates 
of motion; the fact that the stars had actually moved 
through considerable distances was, however, undeniable. 

Observations made since the time of Halley, with im- 
proved instruments, show that many other stars have an 
apparent proper motion, though but few have been discov- 
ered whose annual change of position exceeds a single 
second of arc. Of these the following are some of the 
most conspicuous. The star 1830 of Groombridge's cata- 
logue moves at the rate of more than 7" per year ; the star 
\i Cassiopeia? moves more than half as fast ; and the star 
a Oentauri has a motion nearly equal to that of \i Cas- 
siopeiae. 

Among the rapidly moving double stars we may mention 
61 Cygni, whose components are separated by an arc of 
about 15". It is found that the apparent proper motion of 
each of the components is more than 5" a year, but that the 
distance between them remains unchanged. 

Secchi, in speaking of the relation between proper mo- 
tions and magnitudes, says that there are some quite small 
stars that have a large proper motion ; but when a great 
number of stars are considered, he lays it down as a general 
rule that the largest stars have the largest proper motions, 
and for equal magnitudes that double stars have a greater 
proper motion than single ones. 

The directions in which different stars are moving are 
widely different. Mr. Proctor, who has bestowed much at- 
tention on the subject, thinks that he has discovered a ten- 
dency among stars belonging to certain natural groups to 
move in a common direction. Thus, he finds that five of 
the seven stars forming the dipper, viz., (3, y, 6, e, and £, 
are moving in a common direction, while the other two, a 
and 7], are moving in the opposite direction ; the first five, 
with certain minor companions, constitute a common sys- 
tem to which the other two do not belong. Again, in the 



THE SUE AND THE STARS. 315 

Pleiades about one-half of the stars are moving in a com- 
mon direction, and the remaining ones in an entirely dif- 
ferent direction. 

These various motions are so small that their effects are 
scarcely perceptible in a single generation, but in the course 
of ages they must cause a complete change in the aspect of 
the heavens. 



Applications of Photography. 

250. The relative motions of the stars were, until quite 
recently, determined by the ordinary methods of right 
ascensions and declinations, or else by the aid of the posi- 
tion micrometer. Within a few years, however, the method 
of photography has been gradually coming into use, and for 
many purposes it bids fair to supersede all others. 

Photography has been employed in the investigation of 
solar phenomena, with continually increasing success, for 
more than a quarter of a ceutury. By its use in this direc- 
tion, under the lead of such men as Rutherford and De la 
Rue, new light has been thrown on the question of periodi- 
city in the changes of the sun's surface, eclipse phenomena 
have been investigated, the solar spectrum has been mapped 
even beyond its visible limit, and recently, under the skil- 
ful manipulation of Janssen, photographs of the solar pho- 
tosphere have been obtained, which afford facilities for the 
study of that important envelope that can be attained in no 
other way. 

Its application to the study of the stars received its first 
great impulse in 1864, when Mr. Rutherford began the 
construction of an object-glass which should be corrected 
for actinic or photographic rays in the same way that an 
ordinary objective is corrected for visual rays. When 
finished this lens had an aperture of 11| inches and a focal 
length of nearly 14 feet. Lockyer says : " With this he 
obtained impressions of ninth magnitude stars, and within 



316 ASTRONOMY. 

an area of a square degree in Praesepe in Cancer twenty- 
three stars were photographed in three minutes' exposure. 
Castor gave a strong impression in one second, and stars of 
2" distance showed as double. But even with this method 
Mr. Rutherford was not satisfied. Coming back to the 
llj-inch object-glass which he had used at first, he deter- 
mined to see whether or not the addition of a meniscus 
lens outside the front lens would not give him the requisite 
shortness of focus and bring the actinic rays absolutely 
together. By this arrangement, he got a telescope which 
can be used for all purposes of astronomical research, and 
he has also eclipsed all his former photographic efforts." 

To describe the details of photographing groups and 
clusters would exceed our assigned limits ; suffice it to say, 
that his process enabled him to obtain impressions of stars 
down to the tenth magnitude with such distinctness that 
their relative positions could be determined to the greatest 
degree of accuracy by means of an ingenious arrangement 
of powerful microscopes. 

This method of photography cannot fail to be of the 
utmost value to future astronomers in determining the 
apparent motions of the stars. 

Proper Motion of the Sun. 

251. We have seen that many of the stars appear to be 
moving through space, and it is but reasonable to suppose 
that a part, at least, of their seeming motions is due to an 
actual motion of the sun, and consequently of the entire 
solar system. 

If the stars were absolutely at rest and the sun moving in 
a definite direction, it is obvious, from the principles of 
perspective, that the stars would appear to move in paths 
diverging from the point of the celestial sphere toward 
which the sun was moving and converging to the opposite 
point. The stars, however, are not at rest, but are moving, 



THE SUN AND THE STARS. 317 

as we have reason to believe, in every possible direction; it 
seems highly probable that these motions are such as to 
neutralize each other's effects so far as regards the sun's 
proper motion in space. Hence, if we find that the average 
tendency of the stellar motions is away from some definite 
point of the heavens aud toward the opposite point, we may 
fairly infer that the former point is that toward which our 
system is drifting. 

Sir William Herschel investigated the matter in 1783, 
and from the slender data at his command, he concluded 
that the sun is moving toward a point near the star X Her- 
culis. More than half a century later, Argelander, from 
more reliable data, inferred that the sun is moving toward 
a point also in the constellation Hercules, but at a little 
distance from that indicated by Herschel. These conclu- 
sions have been substantially confirmed by the more recent 
investigations of Striive, Galloway, xliry, and other eminent 
astronomers. 

It is now pretty generally conceded that the entire solar 
system is moving toward some point of the constellation 
Hercules ; according to Airy, its annual rate of motion is 
158 millions of miles. 

Distances of the Stars. 

252. It is shown in Art. 70 that the distance of a fixed 
star from the sun is equal to 92,500,000 miles divided by 
the star's annual parallax. Hence, the determination of 
a star's distance must depend upon our ability to measure 
its parallax. In attempting this measurement, astronomers 
have generally directed their attention to those stars which 
have a large proper motion, and which are at the same 
time in the immediate neighborhood of others that have 
no appreciable proper motion, and which are therefore pre- 
sumably without a parallax. 

The ordinary method of proceeding consists in measuring 



318 ASTRONOMY. 

the directions and distances of the star in question from 
two or more of the immovable ones, at all seasons of the 
year, by means of the position micrometer, or by some 
equivalent method ; from these measurements the parallac- 
tic path, and consequently the parallax of the star, may be 
deduced. 

In this manner it has been found that the star a Cen- 
tauri has a parallax of 0".913 ; 61 Cygni has a parallax of 
0".348; a Lyras, one of 0".261; Sirius, one of 0".230; 
Arcturus, one of 0".127 ; and Polaris, one of less than 0".l. 
It is to be noted that the parallaxes above given are only 
approximate. 

A parallax of 1" corresponds to a distance so great that 
it would require 3.22 years for light to traverse it. Hence, 
the stars named above are so far distant that their light 
only reaches us after the following intervals : a Centauri, 
3J years ; 61 Cygni, 9^ years ; a Lyrae, 12^ years ; Sirius, 
14 years ; Arcturus, 25-J- years ; and Polaris, more than 32^- 
years. 

Sir John Herschel, in speaking of the distribution of 
the stars, says that it is but fair to conclude that there are 
innumerable individuals that were visible as stars in the 
great telescope which was employed by his father and him- 
self in gauging the heavens, whose light must have occupied 
2,0.00 years in reaching us. 

Velocity of the Stars. 

253. The actual path of a star in space is generally 
oblique to the line of vision, that is, to the line drawn from 
the star to the observer; we may therefore regard its 
velocity as made up of two components, one at right angles 
to the line of vision and the other coinciding with it. 

The former component can easily be found when we 
know the distance of the star and its corrected proper mo- 
tion, that is, its apparent proper motion corrected for the 



THE SUN AND THE STARS. 319 

actual proper motion of the sun. The only known method 
of finding the latter component is by means of the spectro- 
scope. This method is based on principles that are easily 
understood. 

The color of a homogeneous ray of light, and consequently 
its degree of refrangibility, depends upon the number of 
vibrations that strike the eye in a given time, say in one 
second. If the number of these vibrations is increased in 
any manner, the ray becomes more refrangible, and when 
deviated by a prism it will be thrown forward toward the 
violet end of the spectrum ; if the number of vibrations is 
diminished, the ray becomes less refrangible, and when 
deviated it is thrown backward toward the red end of the 
spectrum. 

Now, let us suppose a star to contain some known ph} 7 si- 
cal element, say hydrogen. If the star is at rest, any one 
of the corresponding dark lines in its spectrum will occupy 
a definite position ; if the star is moving toward the ob- 
server, the number of vibrations that fall upon the prism 
in a second will be increased, and the dark line in question 
will be thrown forward toward the violet end of the spec- 
trum ; if the star is moving aivay from the observer, the 
number of vibrations in a second will be diminished, and 
the dark line will be thrown backward toward the red end 
of the spectrum. 

In any given case, the direction and the amount of dis- 
placement are determined by a comparison spectroscope : 
then, the velocity of the star, either to or from the observer, 
is computed in accordance with the principles of optics. 

The total velocity is equal to the square root of the sum 
of the squares of .its two components. The direction in 
which the star is actually moving may be found by the 
simple principles of geometry. 



320 ASTBOKOMY. 

Spectroscopic Classification of Stars. 

254. Secchi divided the stars into four classes, which he 
called types, the basis of classification being the character 
of their spectra. 

I. The first class embraces the white or azure-tinted 
stars, such as Sirius, a Lyrae, and all the stars of the dip- 
per except a. 

The spectra of these stars are almost continuous, with 
the exception of four strongly marked black lines which are 
the absorption lines of hydrogen ; they also show traces of 
the sodium, magnesium, and iron lines. 

II. The second class includes the yellow stars, such as 
Capella, a Ursae Majoris, Pollux, and the Sun. 

The spectra of these stars are perfectly similar to the 
well-known solar spectrum; they are characterized by a 
great number of fine black lines, among which those of 
sodium, hydrogen, and iron are very conspicuous. 

III. The third class includes the orange-colored and the 
ordinary red stars, such as a Scorpionis, (3 Pegasi, a Her- 
culis, a Orionis, and the like. 

Their spectra are formed of lines and zones, or cloudy 
bands. Secchi says that this kind of spectrum ought to be 
considered as made up of two spectra, one superposed upon 
the other ; one of them is formed of broad zones or- bands 
gradually deepening in cloudiness so as to produce the 
effect of the lights and shades of a fluted column, and the 
other is formed of the black absorption lines of the metals. 

IV. The fourth class embraces the blood-red stars, most 
of which belong to the telescopic magnitudes. 

Their spectra are marked by three bands similar to those 
of the preceding class, but twice as wide. They have, how- 
ever, the brighter and well-defined sides of their channel- 
lings turned toward the violet, whereas in the preceding 
class they are turned toward the red. These spectra some- 
what resemble the spectrum of carbon as seen at the mid- 



THE SUN AND THE STARS. 321 

die of the voltaic arc between two carbon points, except 
that in the stellar spectra the well-defined edges of the 
bands are turned toward the violet, whereas in the carbon 
spectrum they are turned toward the red. 

There are a few stars that are not embraced in any of 
the four classes : of these, the star y Cassiopeia^ gives the 
lines of hydrogen direct, that is, not reversed : this spec- 
trum is not known to be given by any other star in the 
heavens, although something like it was presented by the 
temporary star which appeared in the northern crown in 
the year 1866. 

It is inferred from the nature of these various spectra, as 
compared with those obtained in laboratory work, that stars 
of the first class are much hotter than those of the other 
classes, and that those of the fourth class are of far inferior 
temperature to any of the others, and furthermore that they 
are surrounded by dense vaporous atmospheres. 



Law of Distribution of Stars. 

255. In treating of the distribution of stars, Sir John 
Herschel says: "If we confine ourselves to the three or 
four brightest classes, we shall find them distributed with a 
considerable approach to impartiality over the sphere ; a 
marked preference, however, being observed, especially in 
the southern hemisphere, to a zone or belt following the 
direction of a great circle passing through e Ononis and 
a Crucis. 

"But if we take in the whole amount visible to the 
naked eye, we shall perceive a great increase of number as 
we approach the borders of the Milky Way. And when we 
come to telescopic magnitudes, we find them crowded be- 
yond imagination along the extent of that belt and of the 
branches which it sends off ; so that in fact its whole light 
is composed of nothing but stars of every magnitude, from 



322 ASTRONOMY. 

such as are visible to the naked eye down to the smallest 
point of light perceptible with the best telescopes." 

Form of the Stellar System. 

256. " These phenomena agree with the supposition that 
the stars of our firmament, instead of being scattered indif- 
ferently through space, form a stratum of which the thick- 
ness is small- in comparison with its length and breadth; 
and in which the sun occupies a place somewhere near the 
point where it subdivides into two principal laminae. 

"It is certain that, to an eye so situated, the apparent 
densities of the stars, supposing them to be pretty equally 
scattered through the space they occupy, would be least in 
the direction of a visual ray perpendicular to the lamina, 
and greatest in the directions of its length and breadth, and 
increasing rapidly in passing from one to the other direc- 
tion, just as we see a slight haze in the atmosphere thick- 
ening into a decided fog-bank near the horizon by the rapid 
increase of the mere length of the visual ray. 

" Such is the view of the construction of the starry firma- 
ment taken by Sir William Herschel, whose powerful tele- 
scopes first effected a complete analysis of this wonderful 
zone and demonstrated the fact of its entirely consisting of 
stars. 

" So crowded are they in some parts of it, that by counting 
the stars in a single field of his telescope he was led to con- 
clude that 50,000 had passed under his view in a zone two 
degrees in breadth during a single hour's observation. 

" In that part of the milky way which is situated in 10 
hours 30 minutes of right ascension, and between the 147th 
and the 150th degree of north polar distance, upwards of 
5,000 stars have been reckoned to exist in a square degree. 
The immense distances at which the remoter regions are 
situated will sufficiently account for the vast preponderance 
of small magnitudes which are observed in it." 



THE SUN AND THE STARS. 323 



The Nebular Hypothesis. 



257. The nebular hypothesis is an explanation of the 
manner in which the solar system may have been evolved 
from a vast nebula by the action of known forces. The 
fundamental idea of the theory was elaborated by Kant, but 
it owes most of its scientific importance to the reasoning 
of La Place, whose name it usually bears. 

According to this eminent scientist, the sun was, at some 
remote epoch, the central nucleus of an intensely heated 
nebula, extending to a distance greater than the remotest 
planet, and having a general motion of rotation from west 
to east. As this fiery mass cooled down it would contract 
in volume, and as a consequence its augular velocity would 
increase. 

A time would ultimately come when the centrifugal 
forces acting on its outer molecules would exactly balance 
the central forces of attraction ; then, as the process of 
contraction went on, these molecules would be left behind, 
forming a great equatorial ring revolving around ^the in- 
terior nucleus. 

At subsequent epochs, and for similar reasons, other 
separations w T ould take place, giving rise to a succession of 
distinct rings, all revolving in the same direction and situ- 
ated very nearly in one plane. 

The rings thus formed, with a single exception, were 
supposed to be made up of matter unequally distributed ; 
consequently, in cooling down they would contract irregu- 
larly and would finally break up into unequal fragments, 
all revolving in the same direction as the original nebula ; 
in each case, the largest fragment would attract to itself 
all the others belonging to the same ring, and in this way 
there would result a number of revolving nebulous masses 
which would slowly condense into planets. In the excep- 
tional case the matter may have been more uniformly dis- 
tributed, so that the contraction would be more regular, 



324 ASTRONOMY. 

and the fragments into which it separated would be more 
nearly equal ; these fragments, condensing around separate 
centres, would form a ring, or zone, of planetoids. 

The planets, in condensing from their vaporous condition, 
would experience changes analogous to those that were 
supposed to have taken place in the original nebula ; these 
changes are supposed to have resulted in the formation of 
the various satellites and the ring of Saturn. 

Admitting that the assumed transformations are in 
accordance with mechanical and physical laws, of which 
there is considerable doubt, this theory of the evolution of 
the solar system would explain many observed facts. Thus, 
it would explain why the planets and planetoids revolve in 
the same direction that the sun turns on its axis; but it is 
difficult to see how it would account for the great inclina- 
tions of the planes of axial rotation, very strongly marked 
in the cases of the Earth, Mars, and Saturn, and still more 
conspicuous in the cases of Uranus and Neptune. It 
would explain why the angular velocities of the planets 
increase as their distances from the sun diminish ; but it 
would totally fail to account for the fact that the angular 
velocity of the inner satellite of Mars is more than three 
times that of the planet itself. 



CLASSIFIED INDEX. 



Aberration of light, 93. 
Achromatic, 19. 
Adams, Neptune, 267. 
Aerolites, 298, 308. 

" remarkable falls, 311. 
Algol, variable star, 52. 
Annual parallax, 91. 
Anomalistic year, 138. 
Anomaly, 137. 
Aphelion, 62. . 
Apogee, 118. 
Apparent semi-diameter, 121. 

" solar time, 105. 
Applications of photography, 315. 
Apsides, line of, 62. 
Aspects of heavens, 53. 
Astronomical clock, 18. 
" dates, 108. 

" telescope, 19. 

Triangle. 103. 
units, 109. 
Astronomy, 8. 
Augustan correction, 214. 
Axis of the earth and heavens, 9. 
Azimuth of a body, 10. 



Baily's beads, 187. 
Bayer, names of stars, 31. 
Belt of Orion, 39. 
Biela's comet, 286. 
Binary stars, 44. 
Bissextile year. 214. 
Bore, tidal, 209. 
Brightness of stars. 27. 
Bulwark plains, 131. 



Calendar, 210. 
Calendar, civil, 210, 212. 
44 ecclesiastical, 217. 
44 Gregorian, 215. 
Julian, 213. 
Catalogues of stars. 28. 
Cavendish apparatus, 79. 
Celestial sphere, 8. 
Changes of seasons, 83. 
Chromosphere, 166. 
Chronograph, 112. 
Chronological cycles, 221. 
Chronometer, 109. 
Circle of perpetual apparition. 56. 
44 '• occupation, 56. 

Ciicumpolar stars. 32. 
Clock, astronomical, 18. 

error of, 110. 
Clusters of stars, 45. 
Collimation. line of, 20. 
Colored stars, 51. 
Coluics. 14. 
Comets, 270. 

44 brilliancy, 274. 

coma, 273. 
44 curvature of tail, 278. 
44 description of, 272. 
disintegration of, 286. 
distribution of, 283. 
head. 273. 
4 " mass and tenuity, 275. 
44 number of, 272. 
44 remarkable, 287. 
tails of. 277. 
volumes of, 281. 
Comparison of time. 108. 
Conjunction, 69. 

inferior. 69. 



326 



CLASSIFIED INDEX. 



Conjunction, superior, 69. 
Constellations, 30. 

li northern, 32. 

" southern, 32. 

" zodiacal, 31. 

Corona of sun, 170. 
Correction of clock, 18. 
Cracks on mpon, 133. 
Cycle, lunar, 217. - 
" of induction, 222. 
" solar, 219. 



Day, sidereal, 17. 

" solar, 105. 

" tidal, 204, 

Declination, 16. 

" circle, 14. 

u method of finding, 26. 

Delisle's method of finding solar paral- 
lax, 146. 
Density of earth, 81. 
Dionysian period, 223. 
Dipper, 34. 
Dissociation, 154. 
Distances of stars, 317. 
Distribution of sun-spots, 165. 
Diurnal motion, 8. 

" inequality, 202. 
Dominical letter, 219. 
Donati's comet, 290. 
Double stars, 44. 



Earth, density, 81. 

" dimensions, 75. 

" distance from sun, 145. 

11 ellipticity, 76. 

" form, 73. 
Easter, 217. 
Eccentricity, 62. 
Eclipse, 175. 

" annular, 177. 

" central, 177. 
cycle, 177. 

" duration of, 185. 

" general, of sun, 182. 
kinds of, 177. 

" local, of sun, 181. 

" lunar, 175. 

" magnitude, 181. 

" partial, 177. 

14 phenomena, 185. 

" seasons, 191. 



Eclipse, solar, 175. 

total, 177, 188. 
visibility, 190. 
Ecliptic, 12. 

" limits, 188. 
" lunar, 189. 

obliquity of, 136. 
" solar, 177. 
Elements of comet's orbit, 272. 
" planet's orbit, 142. 

Elongation, 69. 

" of Mercury, 226. 

" of Venus, 230. 

Encke's comet, 295. 
Envelopes of comet, 279. 

" sun, 153. 

Epact, 218. 

Equation of time, 106. 
Equator, 11. 
Equatorial protuberance, 76. 

" telescope, 23. 
Equinoctial, 11. 
Equinoxes, 12. 

" line of, 13. 

" precession of, 13, 95. 

Establishment of a port, 205. 
Evening and morning star, 230. 
Eye-piece, 20. 



Faculse, 160. 
Fire-balls, 298, 305. 

(i 

Galaxy, 43. 

Geocentric latitude, 104. 

" longitude, 104. 

" parallax, 89. 

" place, 135. 

Geographic latitude, 104. 
Globe, celestial, 28. 
Golden number, 217. 
Gravitation, law of, 71. 
Gregorian calendar, 215. 

H 

Hall, satellites of Mars, 239. 
Halley's comet, 287. 

" method of parallax, 145. 
Harvest moon, 128. 
Heavenly bodies, 7. 
Heliocentric latitude, 68. 
" longitude, 68. 



CLASSIFIED INDEX. 



327 



Heliocentric parallax, 89. 

" place, 135. 

Herschel, Uranus, 264. 

" distribution of stars, 321. 
4i form of stellar system, 322. 
Horizon, 10. 
Horizontal plane, 9. 

" parallax, 90. 

Hour angle, 15. 
•' circle, 14. 
Hyades, cluster, 38. 



Inclination of orbit, 70. 

Inferior planets. 60. 

Irregularities of planetary motion. 140. 



Jupiter, distance from sun, 243. 
" magnitude, 242. 
" periodic rime, 243. 
" rotation, 245. 
satellites, 247. 
" synodic period, 243. 
" telescopic appearance. 244. 
Julian calendar, 213. 
period, 222. 



Kepler's laws, 71. 



Latitude of place, 11. 
" celestial, 68. 
" geocentric, 104. 
" geographic, 104. 
" methods of finding, 102. 
Leap year, 215. 
Leverrier, Neptune, 268. 
Librations of moon, 125. 
Light, velocity of, 92, 251. 
Line of apsides, 62. 
" collimation, 20. 
" equinoxes, 13. 
" nodes, 70. 
Local time. 109. 
Longitude of place, 111. 
" celestial, 68. 

* l geocentric, 68. 

heliocentric, 68. 
methods of finding, 113. 



Lunar cycle, 217. 
11 distances, 114. 
" eclipses, 175, 188. 
" month, 121. 
" periods, 124. 

M 

Magnifying power. 21. 
Magnitude of stars, 27. 
Mars, brilliancy, 236. 
" distance from sun, 235. 
" magnitude, 235. 
" periodic time, 235. 
" rotation, 237. 
" satellites, 239. 
" synodic period, 236. 
11 telescopic appearance 237. 
Mass of sun, 150. 

" planets, 151. 
Mean longitude of sun, 106. 
" solar time, 105. 
" sun, 106. 
Mercury, 225. 

" distance from sun, 225. 

" elongation, 226. 

" magnitude, 225. 

" periodic time, 225. 

" phases, 227. 

" synodic period, 226. 

" telescopic appearance, 227; 

" transits, 228. 

" visibility, 226. 

Meridian, 10. 

" circle, 25. 

Meteoric showers, 298. 
" streams, 299. 
Meteorites, 297. 

remarkable falls, 311. 
Meteors, August, 303. 

heights of, 304. 
" November, 300. 
Micrometer, filar, 98. 

" position, 99. 

Milky way. 43. 
Mir a, variable star, 52. 
Month, calendar, 210. 

lunar, 121. 
Moon, distance of, 118. 

" irregularity of motion, 119. 
" librations, 125. 
" magnitude, 121. 
" path, 117. 
'• periods, 124. 
phases, 127. 



"3-28 



CLASSIFIED INDEX. 



Moon, surface, 129. 
Motions of sun, 12. 

" stars, 58. 

Multiple stars, 44. 



N 



Names of stars, 31. 
Neap tides, 201. 
Nebulee, 46. 

" classes of, 48. 

" distribution of, 50. 
Nebular hypothesis, 323. 
Neptune, discovery, 266. 

" distance from sun, 268. 

" magnitude, 268. 

" periodic time, 268. 

" satellites, 269. 

" synodic period, 268. 
New style, 216. 
Newtonian law, 71. 
Nodical period of sun, 39. 
Nucleus of comet, 273. 
sun, 153. 
" sun-spots, 162. 

Nutation, 97. 



Objective of telescope, 19. 

Oblique sphere, 55. 

Obliquity of ecliptic, 136. 

Occultations, 195. 

Old Style, 216. 

Opposition, 69. 

Orbit, apparent, of sun, 135. 



Parallax, 89. 

" annual, 91. 

" geocentric, 89. 

" heliocentric, 90. 

" luvnjzontal. 90. 

" solar, 149. 
stellar, 92. 
Parallel sphere, 54. 
Penumbra of earth and moon, 175. 

" sun-spot, 162. 

Perigee, 117. 
Perihelion, 62. 
Periodic time, 70. 
Periodicity of sun-spots, 165. 
Perturbations, 71. 
Phases of moon, 121. 



Photosphere, 159. 
Planetoids, 59, 241. 
Planets, 59. 

inferior, 60. 

" superior, 60. 
Pleiades, cluster, 45. 
Pointers, 35. 
Polar circles, 57. 

" distance, 16. 
Polaris, 35. 

Poles of earth and heavens, 9. 
Precession of equinoxes, 95. 
Prime meridian, 111. 

" vertical, 10. 
Principles of spectrum analysis, 157. 
Proper motions of stars, 68, 313. 

" " sun, 316. 

Protuberance, equatorial, 76. 
Protuberances, solar, 168. 
Pyramids, 98. 



R 

Radiant point of meteors, 303. 
Radius-vector, 62. 
Rate of clock, 18. 
Reflecting telescope, 21. 
Refracting telescope, 19. 
Refraction, 84. 

" atmospheric, 85. 

Relative orbit of moon, 180. 
Resisting medium, 296. 
Reticle, 20. 

Retrograde motion, 59. 
Reversing layer, 167. 
Right ascension, 15. 

" method of finding, 24. 
Right sphere, 53. 
Ring mountains, 131. 
Rings of Saturn, 254. 



S 

Saroc, 193. 
Satellites, 59. 

" of Mars, 239. 
of Jupiter, 247. 
of Saturn, 262. 
" of Uranus, 265. 

of Neptune, 269. 
Sauirn, 252. 

" disappearance of rings, 
" distance from sun, 252. 
" . magnitude, 253. 
u periodic. Lime, 252. 



CLASSIFIED 1XDEX. 



329 



Saturn, rings, 254. 
" rotation, 253. 
satellites, 262. 
" synodic period, 252. 
" telescopic appearance, 2.53. 
Schwabe, sun-spots, 166. 
Seasons, 81. 
Shooting stars, 298. 
Sidereal day, 16. 
" period, 117. 

time, 16. 
" year, 138. 
Signs of zodiac, 31. 
Solar corona, 170- 
" cycle, 219. 
iv parallax, 145. 
'• periods, 138. 
" system, 59. 
" time, 105. 
Solstices, 14. 
Spectroscope, 154. 

Spectroscopic classification of stars, 320. 
Sphere, celestial, 8. 
" oblique, 55. 
" parallel, 54. 
right, 53. 
Spheroidal form of earth, 65. 
Spiral nebulae, 48. 
Spring tides, 201. 
Stars, 27. 
" catalogues, 28. 
'• classification, 27. 
" clusters, 45. 
" double, 44. 
;t maps, 27. 
" names, 31. 
" parallax, 92. 
" proper motions, 58. 
" spectroscopic classification, 320. 
Stellar system, form, 322. 
Sun, constitution of, 153. 
" distance of, 149. 
" heat of, 151. 
" magnitude, 150. 
" motions of, 12. 
" place in system, 135. 
" rank among the stars, 313. 
" spots, 161. 
Superior conjunction, 69. 

planets, 60. 
Synodic period, 7. 



Tables of elements, 65, 66, 71. 
Telescope, 19. 



Tidal wave, 198. 
Tides. 197. 

•' apogean, 202. 
" causes, 197. 
" distribution, 199. 
'• diurnal inequality, 202. 
" modification of, 206. 
perigean, 202. 
priming and lagging, 203. 
" spring and neap, 201. 
variations in, 201. 
Time, local, 109. 
sidereal, 16. 
solar, 105. 
Torsion balance, 77. 
Transit, instrument, 23. 
lower, 14. 
" upper, 14. 
Transits of Mercury, 228. 

Venus, 233. 
Tropical year. 138. 
Tropic of Cancer, 57. 

" Capricorn, 57. 
Twilight, 88. 



Unit of distance, 73. 

14 mass, 73. 

" time, 73. 
Uranus, 264. 

" discovery, 264. 

" distance from sun, 264. 

" magnitude, 265. 

" periodic time, 264. 

" satellites, 265. 

" synodic period, 265. 



Variable stars, 52. 
Velocity f light, 149, 251. 

" stars, 318. 

Venus, 229. 

" brilliancy. 230. 

11 distance from sun, 229. 

" elongation, 230. 

" magnitude, 229. 

" periodic time, 229. 

" phases, 230. 

" synodic period, 229. 

" telescopic appearance, ! 

" transits of, 233. 
visibility, 230. 
Vernal equinox, 12. 



330 



CLASSIFIED INDEX. 



Vertical line, 9. 
Vertical plane, 10. 
Visibility of eclipses, 190. 



W 



Week, 211. 

k ' days of, 212. 



Year, anomalistic, 138. 



Year, sidereal, 138. 
" tropical, 138. 



Zenith, 9. 

" distance, 10. 

" telescope, 100. 
Zodiac, 31. 

" constellations of, 31. 

" signs of, 31. 
Zodiacal light, 173. 



BARNES'S POPULAR HISTORY 
OF THE UNITED STATES. 



By the author of Barnes's "Brief Histories for Schools." Complete in one superb 
royal octavo volume of 800 pages. Illustrated with 320 wood engravings and 14 steel 
plates, covering the period from the Discovery of America to the Accession of President 
Arthur. 

Part I. Colonial Settlement ; Exploration ; Conflict ; Manners ; Customs ; Educa- 
tion ; Religion, &c, &c. , until political differences with Great Britain threatened open 
rupture. 

Part II. Resistance to the Acts of Parliament ; Resentment of British Policy, and 
the Succeeding War for American Independence. 

Part III. From the Election of President Washington to that of President Lincoln, 
with the expansion and growth of the Republic ; its Domestic Issues and its Foreign 
Policv. 

Part IV. The Civil War and the End of Slavery. 

Part V. The New Era of the Restored Union ; with Measures of Reconstruction ; 
the Decade of Centennial Jubilation, and the Accession of President Arthur to Office. 

Appendix. Declaration of Independence ; The Constitution of the United States 
and its Amendments ; Chronological Table and Index ; Illustrated History of the 
Centennial Exhibition at Philadelphia. 

The wood and steel engravings have been expressly chosen to illustrate the customs of 
the periods reviewed in the text. Ancient houses of historic note, and many portraits of 
early colonists, are thus preserved, while the elaborate plans of the Exposition of 1876 
ai-e fully given. The political characteristics of great leaders and great parties, which 
had been shaped very largely by the issues which belonged to slavery and slave labor, 
have been dealt with in so candid and impartial a manner as to meet the approval of 
all sections of the American people. The progress of science, invention, literature, and 
art is carefully noted, as well as that of the national physical growth, thus condensing 
into one volume material which is distributed through several volumes in larger works. 
Outline maps give the successive stages of national expansion, and special attention 
has been given to those battles, by land and sea, which have marked the military growth 
of the republic. Sgp^ Specially valuable for reference in schools and households. 

From Prof. S. T. Dutton, Superintendent 
of Schools, New Haven, Conn. 

" It seems to me to be one of the best 
and most attractive works of the kind I 
have ever seen, and it will be a decided 
addition to the little libraries which we 
have already started in our 'larger 
schools." 



From Prof. F. F. Barrows, Brown School, 
Hartford, Conn. 
" Barnes's Popular History has been in 
our reference library for two years. Its 
concise and interesting presentation of 
historical facts causes it to be so eagerly 
read by our pupils, that we are obliged to 
duplicate it to supply the demand for its 
use." 

From Hon. John R. Buck. 
" I concur in the above." 

From Hon. J. C. Stockwell. 
" I heartily concur with Mr. Barrows in 
the within commendation of ' Barnes's 
Popular History,' as a very interesting and 
instructive book of reference." 
From A. Morse, Esq. 
" I cordially concur in the above." 
From Rev. Wm. T. Gage. 

th the opinions 



"I heartily agree 
above expressed." 

From David Crary, Jr. 

" The best work for the purpose pub- 
lished." 



From Prof. War. Martin, of Beattystown, 
N.J. 
' ' This volume is well adapted to the 
wants of the teacher. A concise, well- 
arranged summary of events, and just the 
supplement needed by every educator who 
teaches American history." 

From Prof. C. T. R. Smith, Principal of 

the Lansingburgh, N. Y., Academy. 

"In the spring I procured a copy of 
' Barnes's Popular History of the United 
States,' and have used it daily since, in 
preparing my work with my class in Ameri- 
can history, with constantly increasing 
admiration at the clearness, fairness, and 
vividness of its style and judicious selec- 
tion of matter." 

Prices. Cloth, plain edge, $5.00; cloth, richly embossed, gilt edge, $6.00; sheep, 
marble edge, $7.00 ; half calf, $8.00 ; half morocco, $8.00 ; full morocco, gilt, $10.00. 




P3 ~ 

fe 3 
* fe 



<! O 



SCHOOL AND COLLEGE TEXT-BOOKS. 

♦ 

The National Series Readers and Spellers, 



THE NATIONAL READERS, 



By PARKEE and WATSON. 



No. I. — National Primer .... 


. 64 pp 


16° 


No. 2. — National First Reader . . 


. . 128 " 


16° 


No. 3. — National Second Reader . 


. . 224 " 


16° 


No. 4. — National Third Reader 


. . 288 " 


12° 


No. 5. — National Fourth Reader . 


. 432 " 


12° 


No. 6. — National Fifth Reader . 


; . 600 " 
. 160 pp 


12° 


National Elementary Speller . . 


16° 


National Pronouncing Speller . . 


. 188 " 


12° 



THE INDEPENDENT READERS, 



By J. MADISON WATSON. 



The Independent First ( Pri £ ary ) Reader 


80 pp 


.16° 


The Independent Second Reader . . 


160 " 


16° 


The Independent Third Reader . . 


240 " 


16° 


The Independent Fourth Reader . . 


264 " 


12° 


The Independent Fifth Reader . . . . 


336 "• 


12° 


The Independent Sixth Reader . . . 


474 " 


12° 


The Independent Complete Speller . 


162 " 


16° 



The Independent Child's Speller (Script) 80 pp. 16° 
The Independent Youth's Speller {Script) 168 " 12° 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

WATSON'S INDEPENDENT 
READERS. 



This Series is designed to meet a general demand for smaller and cheaper 
books than the National Series proper, and to serve as well for intermediate 
volumes of the National Readers in large graded schools requiring more books 
than one ordinary series will supply. 

Beauty. — The most casual observer is at once impressed with the unpar- 
alleled mechanical beauty of the Independent Readers. The Publishers be- 
lieve that the aesthetic tastes of children may receive no small degree of 
cultivation from their very earliest sohool-books, to say nothing of the impor- 
tance of making study attractive by all such artificial aids that are legitimate. 
In accordance with this view, not less than $25,000 was expended in their 
preparation before publishing, with a result which entitles them to be con- 
sidered " the perfection of common-school books." 

Selections. — They contain, of course, none but entirely new selections. 
These are arranged according to a strictly progressive and novel method of 
developing the elementary sounds in order in the lower numbers, and in all, 
with a view to topics and general literary style. The mind is thus led in fixed 
channels to proficiency in every branch of good reading, and the evil results of 
"scattering," as practised by most school-book authors, avoided. 

The Illustrations, as may be inferred from what has been said, are ele- 
gant beyond comparison. They are profuse in every number of the series, from 
the lowest to the highest. This is the only series published of which this 
is true. 

The Type is semi-phonetic, the invention of Professor Watson. By it every 
letter having more than one sound is clearly distinguished in all its variations 
without in any way mutilating or disguising the normal form of the letter. 

Elocution is taught by prefatory treatises of constantly advancing grade 
and completeness in each volume, which are illustrated by woodcuts in the 
lower books, and by blackboard diagrams in the higher. Professor Watson 
is the first to introduce practical illustrations and blackboard diagrams for 
teaching this branch. 

Foot-Notes on every page afford all the incidental instruction which the 
teacher is usually required to impart. Indices of words refer the pupil to the 
place of their first use and definition. The biographies of authors and others 
are in every sense excellent. 

Economy. — Although the number of pages in each volume is fixed at the 
minimum, for the purpose recited above, the utmost amount of matter avail- 
able without overcrowding is obtained in the space. The pages are much 
wider and larger than those of any competitor and contain twenty per cent 
more matter than any other series of the same type and number of pages. 

All the Great Features. — Besides the above all the popular features of 
the National Readers are retained except the word-building system. The 
latter gives place to an entirely new method of progressive development, based 
upon some of the best features of the word system, phonetics, and object 
lessons. 

6 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

PARKER & WATSON'S NATIONAL 
READERS. 



The salient features of these works which have combined to render them so popular 
may he briefly recapitulated, as follows : — 

i. THE WORD-BUILDING SYSTEM. — This famous progressive method 
for young children originated and was copyrighted with these books. It constitutes a 
process with which the beginner with words ot' one letter is gradually introduced to 
additional lists formed by prefixing or affixing single letters, and is thus led almost 
insensibly to the mastery of the more difficult constructions. This is one of the most 
striking modern improvements in methods of teaching. 

2. TREATMENT OF PRONUNCIATION. — The wants of the youngest 
scholars in this department are not overlooked. It may be said that from the first 
lesson the student by this method need never be at a loss for a prompt and accurate 
rendering of every word encountered. 

3. ARTICULATION AND ORTHOEPY are considered of primary importance. 

4. PUNCTUATION is inculcated by a series of interesting reading lessons, the 
simple perusal of which suffices to fix its principles indelibly upon the mind. 

5. ELOCUTION. —Each of the higher Readers (3d, 4th, and 5th) contains elabo- 
rate, scholarly, and thoroughly practical treatises on elocution. This feature alone has 
secured for the series many of its warmest friends. 

6. THE SELECTIONS are the crowning glory of the series. Without excep- 
tion it may be said that no volumes of the same size and character contain a collection 
so diversified, judicious, and artistic as this. It embraces the choicest gems of Eng- 
lish literature, so arranged as to afford the reader ample exercise in every department 
of style. So acceptable has the taste of the authors in this department proved, not 
only to the educational public but to the reading community at large, that thousands 
of copies of the Fourth and Fifth Readers have found their way into public and private 
libraries throughout the country, where they are in constant use as manuals of litera- 
ture, for reference as well as perusal. 

7. ARRANGEMENT. —The exercises are so arranged as to present constantly 
alternating practice in the different styles of composition, while observing a definite 
plan of progression or gradation throughout the whole. In the higher books the 
articles are placed in formal sections and classified topically, thus concentrating the 
interest and inculcating a principle of association likely to prove valuable in subse- 
quent general reading. 

8. NOTES AND BIOGRAPHICAL SKETCHES. — These are full and ade- 
quate to every want. The biographical sketches present in pleasing style the history of 
every author laid under contribution. 

9. ILLUSTRATIONS. —These are plentiful, almost profuse, and of the highest 
character of art. They are found in every volume of the series as far as and including 
the Third Reader. 

10. THE GRADATION is perfect. Each volume overlaps its companion pre- 
ceding or following in the series, so that the scholar, in passing from one to another, is 
only conscious, by the presence of the new book, of the transition. 

11. THE PRICE is reasonable. The National Readers contain more matter than 
any other series in the same number of volumes published. Considering their com- 
pleteness and thoroughness, they are much the cheapest in the market. 

12. BINDING. — By the use of a material and process known only to themselves, 
in common with all the publications of this house, the National Readers are warranted 
to outlast any with which they may be compared, the ratio of relative durability 
being in their favor as two to one. 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



SUPPLEMENTARY READING. 



Monteith's Popular Science Reader. 

James Monteith, author of Monteith's Geographies, has here presented a Supple- 
mentary Reading Book expressly for the work of instruction in reading and science at 
one and the same time. It presents a number of easy and interesting lessons on Natural 
Science and Natural History, interspersed with appropriate selections in prose and 
poetry from standard authors, with blackboard drawing and written exercises. It 
serves to instil the noblest qualities of soul and mind, without rehearsing stories of 
moral and mental depravity, as is too often done in juvenile books. The book is elabo- 
rately illustrated with fine engravings, and brief notes at the foot of each page add to 
the value and teachableness of the volume. 12mo, half bound, 360 pages. 

The Standard Supplementary Readers. 

The Standard Supplementary Readers (formerly Swinton' t s Supplementary Readers), 
edited by William Swinton and George R. Cathcart, have been received with marked 
favor in representative quarters from Maine to California. They comprise a series of 
carefully graduated reading books, designed to connect with any series of school Readers. 
They are' attractive in appearance, are bound in cloth, and the first four books are 
profusely illustrated by Fredericks, White, Dielman, Church, and others. The six books, 
which are closely co-ordinated with the several Readers of any regular series, are : — 

1. Easy Steps for Little Feet. Supplementary to First Reader. 

In this book the attractive is the chief aim, and the pieces have been written and 
chosen with special reference to the feelings and fancies of early childhood. 128 pages, 
bound in cloth and profusely illustrated. 

2. Golden Book of Choice Reading. Supplementary to Second 

Reader. 
This book represents a great variety of pleasing and instructive reading, consisting of 
child-lore and poetry, noble examples and attractive object-reading, written specially for it. 
192 pages, cloth, with numerous illustrations. 

3. Book Of Tales. Being School Readings Imaginative and Emotional. 

Supplementary to Third Reader. 
In this book the youthful taste for imaginative and emotional is fed with pure and noble 
creations drawn from the literature of all nations. 272 pages, cloth. Fully illustrated. 

4. Readings in Nature's Book. Supplementary to Fourth Reader. 
This book contains a varied collection of charming readings in natural history and 

botany, drawn from the works of the great modern naturalists and travellers. 352 pages, 
"loth. Fully illustrated. 

5. Seven American Classics. 

6. Seven British Classics. 

The " Classics " are suitable for reading in advanced grades, and aim to instil a 
taste for the higher literature, by the presentation of gems of British and American 
authorship. 220 pages each, cloth. 

8 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



ORTHOGRAPHY. 

Smith's Series. 

Smith's Series supplies a Speller for every class in graded schools, and comprises 
the most comi>lete and excellent treatise on English Orthography and its companion 
branches extant. 

1. Smith's Little Speller. 

First round in the ladder of learning. 

2. Smith's Juvenile Definer. 

Lessons composed of familiar words grouped with reference to similar significa- 
tion or use, and correctly spelled, accented, and defined. 

3. Smith's Grammar-School Speller. 

Familiar words, grouped with reference to the sameness of sound of syllables dif- 
ferently spelled. Also definitions, complete rules for spelling and formation of deriva- 
tives, and exercises in false orthography. 

4. Smith's Speller and Definer's Manual. 

A complete School Dictionary, containing 14,000 words, with various other useful 
matter in the way of rules and exercises. 

5. Smith's Etymology — Small and Complete Editions. 

The first and only Etymology to recognize the Anglo-Saxon our mother tongue; 
containing also full lists of derivatives from the Latin, Greek, Gaelic, Swedish, Norman, 
&c. , &c. ; being, in fact, a complete etymology of the language for schools. 

Northend's Dictation Exercises. 

Embracing valuable information on a thousand topics, communicated in such a 
manner as at once to relieve the exercise of spelling of its usual tedium, and combine 
it with instruction of a general character calculated to profit and amuse. 

Phillip's Independent Writing Spellers. 

1. Primary. 2. Intermediate. 3. Advanced. 

Unquestionably the best results can be attained in writing spelling exercises. This 
series combines with written exercise a thorough and practical instruction in penman- 
ship. Copies in capitals and small letters are set on every page. Spaces for twenty 
words and definitions and errors are given in each lesson. In the advanced book there 
is additional space for sentences. In practical life we spell only when we write. 

Brown's Pencil Tablet for Written Spelling. 

The cheapest prepared pad of ruled blanks, with stiff board back, sufficient for 
64 lessons of 25 words. 

Pooler's Test Speller. 

The best collection of " hard words " yet made. The more uncommon ones are fully 
defined, and the whole are arranged alphabetically for convenient reference. The book 
is designed for Teachers' Institutes and " Spelling Schools," and is prepared by an 
experienced and well-known conductor of Institutes. 

Wright's Analytical Orthography. 

This standard work is popular, because it teaches the elementary sounds in a 
plain and philosophical manner, and presents orthography and orthoepy in an easy, 
uniform system of analysis or parsing. 

9 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



ORTHOGRAPHY — Continued. 

Barber's Complete Writing Speller. 

" The Student's Own Hand-Book of Orthography, Definitions, and Sentences, con- 
sisting of Written Exercises in the Proper Spelling, Meaning, and Use of Words." 
(Published 1873. ) This differs from Sherwood's and other writing spellers in its more 
comprehensive character. Its blanks are. adapted to writing whole sentences instead 
of detached words, with the proper divisions for numbering, corrections, &c. Such 
aids as this, like Watson's Child's Speller and Phillip's Writing Speller, find their 
raison d'etre in the postulate that the art of correct spelling is dependent upon written, 
and not upon spoken language, for its utility, if not for its very existence. Hence 
the indirectness of purely oral instruction. 



ETYMOLOGY. 

Smith's Complete Etymology. 
Smith's Condensed Etymology. 

Containing the Anglo-Saxon, French, Dutch, German, Welsh, Danish, Gothic, Swedish, 
Gaelic, Italian, Latin, and Greek roots, and the English words derived therefrom 
accurately spelled, accented, and defined. 



From Hon. Jno. G. McMynn, late State 

Superintendent of Wisconsin. 

" I wish every teacher in the country 
had a copy of this work." 

From Prof. C. H. Vereill, Pa. State 

Normal School. 

"The Etymology (Smith's) which we 
procured of you we like much. It is the 
best work for the class-room we have 
saen." 



From Prin. Wm. F. Phelps, Minn. State 
Normal. 

"The book is superb — just what is 
needed in the department of etymology 
and spelling." 

From Hon. Edward Ballard, Supt. of 
Common Schools, State of Maine. 

,e The author has furnished a manual of 
singular utility for its purpose." 



DICTIONARY. 

Williams's Dictionary of Synonymes ; 

Or, Topical Lexicon. This work is a School Dictionary, an Etymology, a compilation 
of Synonymes, and a manual of General Information. It differs from the ordinary lexicon 
in being arranged by topics, instead of the letters of the alphabet, thus realizing the 
apparent paradox of a " Readable Dictionary." An unusually valuable school-book. 

Kwong's Dictionary of English Phrases. 

With Illustrative Sentences, collections of English and Chinese Proverbs, transla- 
tions of Latin and French Phrases, historical sketch of the Chinese Empire, a chrono- 
logical list of the Chinese Dynasties, brief biographical sketches of Confucius and 
of Jesus, and complete index. Bjr Kwong Ki Chiu, late Member of the Chinese Edu- 
cational Mission in the United States, and formerly principal teacher of English in the 
Government School at Shanghai, China. 9C0 pages. 8vo. Cloth. 

From the Hartford Courant : " The volume is one of the most curious and interest- 
ing of linguistic works." 

From the New York Nation : "It will amaze the sand-lot gentry to be informed that 
this remarkable work will supplement our English dictionaries even for native Americans." 

10 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



ENGLISH GRAMMAR, 



SILL'S SYSTEM. 
Practical Lessons in English. 

A brief course in Grammar and Composition. By J. M. B. Sill. This beautiful 
book, by a distinguished and experienced teacher, at once adopted for exclusive use 
in the State of Oregon and the city of Detroit, simply releases English Grammar 
from bondage to Latin and Greek formulas. Our language is worthy of being taught 
as a distinct and independent science. It is almost destitute of inflections and yet 
capable of being systematized, and its study may certainly be simplified if treated by 
itself and for itself alone. Superintendent Sill has cut the Gordian knot and leads 
the van of a new school of grammarians. 



CLARK'S SYSTEM. 
Clark's Easy Lessons in Language 

Contains illustrated object-lessons of the most attractive character, and is couched 
in language freed as much as possible from the dry technicalities of the science. 

Clark's Brief English Grammar. 

Part Lis adapted to youngest learners, and the whole forms a complete " brief 
course " in one volume, adequate to the wants of the common school. There is no- 
where published a superior text-book for learning the English tongue than this. 

Clark's Normal Grammar. 

Designed to occupy the same grade as the author's veteran " Practical " Grammar, 
though the latter is still furnished upon order. The Normal is an entirely new treatise. 
It is a full exposition of the system as described below, with all the most recent im- 
provements. Some of its peculiarities are, — a happy blending of Syntheses with 
Analyses ; thorough criticisms of common errors in the use of our language ; and 
important improvements in the syntax of sentences and of phrases. 

Clark's Key to the Diagrams. 

Clark's Analysis of the English Language. 

Clark's Grammatical Chart. 

The theory and practice of teaching grammar in American schools is meeting with a 
thorough revolution from the use of this system. While the old methods offer profi- 
ciency to the pupil only after much weary plodding and dull memorizing, this affords 
from the inception the advantage of practical Object Teaching, addressing the eye by 
means of illustrative figures ; furnishes association to the memory, its most powerful 
aid, and diverts the pupil by taxing his ingenuity. Teachers who are using Clark's 
Grammar uniformly testify that they and their pupils find it the most interesting study 
of the school course. 

Like all great and radical improvements, the system naturally met at first with much 
unreasonable opposition. It has not only outlived the greater part of this opposition, 
but finds many of its warmest admirers among those who could not at first tolerate so 
radical an innovation. All it wants is an impartial trial to convince the most scep- 
tical of its merit. No one who has fairly and intelligently tested it in the school-room 
has ever been known to go back to the old method. A great success is already 
established, and it is easy to prophesy that the day is not far distant when it will be 
the only system of teaching English Grammar. As the System is copyrighted, no other 
text-books can appropriate this obvious and great improvement. 

Welch's Analysis of the English Sentence. 

Remarkable for its new and simple classification, its method of treating connectives, 
its explanations of the idioms and constructive laws of the language, &c. 

11 




z o 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

GEOGRAPHY. 

MONTEITH'S SYSTEM. 

TWO-BOOK SERIES. INDEPENDENT COURSE. 

Elementary Geography. 

Comprehensive Geography (with 103 maps). 

H3P* These volumes are not revisions of old works, not an addition to any series, 
but are entirely new productions, — each by itself complete, independent, comprehen- 
sive, yet simple, brief, cheap, and popular; or, taken together, the most admirable 
" series " ever offered for a common-school course. They present the following features, 
skilfully interwoven, the student learning all about one country at a time. Always 
revised to date of printing. 

LOCAL GEOGRAPHY. — Or, the Use of Maps. Important features of the maps 
are the coloring of States as objects, and the ingenious system for laying down a much 
larger number of names for reference than are lound on any other maps of same size, 
and without crowding. 

PHYSICAL GEOGRAPHY.— Or, the Natural Features of the Earth; illus- 
trated by the original and striking relief maps, being bird's-eye views or photographic 
pictures of the earth's surface. 

DESCRIPTIVE GEOGRAPHY. — Including the Physical; with some account 
of Governments and Races, Animals, &c. 

HISTORICAL GEOGRAPHY. — Or, a brief summary of the salient points of 
history, explaining the present distribution of nations, origin of geographical 
names, &c. 

MATHEMATICAL GEOGRAPHY. — Including Astronomical, which describes 
the Earth's position and character among planets ; also the Zones, Parallels, &c. 

COMPARATIVE GEOGRAPHY. —Or, a system of analogy, connecting new 
lessons with the previous ones. Comparative sizes and latitudes are shown on the 
margin of each map, and all countries are measured in the " frame of Kansas." 

TOPICAL GEOGRAPHY. — Consisting of questions for review, and testing 
the student's general and specific knowledge of the subject, with suggestions for 
geographical compositions. 

ANCIENT GEOGRAPHY. — A section devoted to this subject, with maps, will 
be appreciated by teachers. It is seldom taught in our common schools, because it 
has heretofore required the purchase of a separate book. 

GRAPHIC GEOGRAPHY, or Map-Drawing by Allen's "Unit of Measure- 
ment" system (now almost universally recognized as without a rival), is introduced 
throughout the lessons, and not as an appendix. 

CONSTRUCTIVE GEOGRAPHY. — Or, Globe-Making. With each book a set 
of map segments is furnished, with which each student may make his own gTobe by 
following the directions given. 

RAILROAD GEOGRAPHY. — With a grand commercial map of the United 
States, illustrating steamer and railroad routes of travel in the United States, submarine 
telegraph lines, &c. Also a " Practical Tour in Europe." 



MONTEITH AND McNALLY'S SYSTEM. 

THREE AND FIVE BOOKS. NATIONAL COURSE. 

Monteith's First Lessons in Geography. 
Monteith's New Manual of Geography. 
McNally's System of Geography. 

The new edition of McXally's Geography is now ready, rewritten throughout by 
James Monteith and S. C. Frost. In its new dress, printed from new type, and illus- 
trated with 100 new engravings, it is the latest, most attractive, as well as the most 
thoroughly practical book on geography extant. 

13 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

GEOGRAPHY — Continued. 

INTERMEDIATE OR ALTERNATE VOLUMES IN THE FIVE BOOK SERIES. 

Monteith's Introduction to Geography. 
Monteith's Physical and Political Geography. 

1. PRACTICAL OBJECT-TEACHING. — The infant scholar is first introduced 
to a picture whence he may derive notions of the shape of the earth, the phenomena of 
day and night, the distribution of land and water, and the great natural divisions, 
which mere words would fail entirely to convey to the untutored mind. Other pictures 
follow on the same plan, and the child's mind is called upon to grasp no idea without 
the aid of a pictorial illustration. Carried on to the higher books, this system culmi- 
nates in Physical Geography, where such matters as climates, ocean currents, the 
winds, peculiarities of the earth's crust, clouds and rain, are pictorially explained and 
rendered apparent to the most obtuse. The illustrations used for this purpose belong 
to the highest grade of art. 

2. CLEAR, BEAUTIFUL, AND CORRECT MAPS. — In the lower num- 
bers the maps avoid unnecessary detail, while respectively progressive and affording 
the pupil new matter for acquisition each time he approaches- in the constantly en- 
larging circle the point of coincidence with previous lessons in the more elementary 
books. In the Physical and Political Geography the maps embrace many new and 
striking features. One of the most effective of these is the new plan for displaying on 
each map the relative sizes of countries not represented, thus obviating much confu- 
sion which has arisen from the necessity of presenting maps in the same atlas drawn 
on different scales. The maps of "McNally'' have long been celebrated for their 
superior beauty and completeness. This is the only school-book in which the attempt 
to make a complete atlas also clear and distinct, has been successful. The map coloring 
throughout the series is also noticeable. Delicate and subdued tints take the place of 
the startling glare of inharmonious colors which too frequently in such treatises dazzle 
the eyes, distract the attention, and serve to overwhelm the names of towns and the 
natural features of the landscape. 

3. THE VARIETY OF MAP-EXERCISE. — Starting each time from a dif- 
ferent basis, the pupil in many instances approaches the same fact no less than six- 
times, thus indelibly impressing it upon his memory. At the same time, this system is 
not allowed to become wearisome, the extent of exercise on each subject being grad- 
uated bv its relative importance or difficulty of acquisition. 

4. THE CHARACTER AND ARRANGEMENT OF THE DESCRIP- 
TIVE TEXT. — The cream of the science has been carefully culled, unimportant 
matter rejected, elaboration avoided, and a brief and concise manner of presentation 
cultivated. The orderly consideration of topics has contributed greatly to simplicity. 
Due attention is paid to the facts in history and astronomy which are inseparably con- 
nected with and important to the proper understanding of s;engraphy, and such only 
are admitted on any terms. In a word, the National System teaches geography as a 
science, pure, simple, and exhaustive. 

5. ALWAYS UP TO THE TIMES. — The authors of these books, editorially 
speaking, never sleep. No change occurs in the boundaries of countries or of counties, 
no new discovery is made, or railroad built, that is not at once noted and recorded, and 
the next edition of each volume carries to every school-room the new order of things. 

6.. FORM OF THE VOLUMES AND MECHANICAL EXECUTION. 
— The maps and text are no longer unnaturally divorced in accordance with the time- 
honored practice of making text-books on this subject as inconvenient and expensive as 
possible. On the contrary, all map questions are to be found on the page opposite the 
map itself, and each book is complete in one volume. The mechanical execution is 
unrivalled. Paper, printing, and binding are everything that could be desired. 

7. MAP-DRAWING. — In 1869 the system of map-drawing devised by Professor 
Jerome Allen was secured exclusively for this series. It derives its claim to original- 
ity and usefulness from the introduction of a fixed unit of measurement applicable to 
every map. The principles being so few, simple, and comprehensive, the subject of 
map-drawing is relieved of all practical difficulty. (In Nos. 2, 2*, and 3, and published 
separately.) 

8. ANALOGOUS OUTLINES. —At the same time with map-drawing was also 
introduced (in No. 2) a new and ingenious variety of Object Lessons, consisting of a 
comparison of the outlines of countries with familiar objects pictorially represented. 

14 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

GEOGRAPHY — Continued. 

9. SUPERIOR GRADATION. —This is the only series which furnishes an avail- 
able volume for every possible class in graded schools. It is not contemplated that a 
pupil must necessarily go through every volume in succession to attain proficiency. 
On the contrary, two will suffice, but three are advised ; and, if the course will admit, 
the whole series should be pursued. At all events, the books are at hand for selection, 
and every teacher, of every grade, can find among them one exactly suited to his class. 
The best combination for those who wish to abridge the course consists of Nos. 1, 2, 
and 3 ; or, where children are somewhat advanced in other studies when they com- 
mence geography, Nos. 1*, 2, and 3. Where bat two books are admissible, Nos. 1* and 
2*, or Nos. 2 and 3, are recoinniended. 




A Sheep Ranch in Montana. 
[Specimen Illustration from McNally's New Geography.] 



15 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

GEOGRAPHY — Continued. 

Monteith's Physical Geography. 

This is a clear, brief statement of the physical attributes of the earth and their rela- 
tions to the heavens. The illustrations and maps are numerous and helpful It pro- 
vides full instruction in this important branch of study in an attractive way for the 
youngest scholars. It contains 54 pages in quarto form. 



MAP-DRAWING. 

Monteith's Map-Drawing Made Easy. 

A neat little book of outlines and instructions, giving the " corners of States " in 
suitable blanks, so that maps can be drawn by unskilful hands from any atlas ; with 
instructions for written exercises or compositions on geographical subjects, and com- 
parative geography. 

Monteith's Manual of Map-Drawing (Allen's System). 

The only consistent plan, by which all maps are drawn on one scale. By its use 
much time may be saved, and much interest and accurate knowledge gained. 

Monteith's Map-Drawing and Object Lessons. 

The last-named treatise, bound with Mr. Monteith's ingenious system for commit- 
ting outlines to memory by means of pictures of living creatures and familiar objects. 
Thus, South America resembles a dog's head ; Cuba, a lizard ; Italy, a boot ; France, a 
coffee-pot ; Turkey, a turkey, &c, &c. 

Monteith's Colored Blanks for Map-Drawing. 

A new aid in teaching geography, which will be found especially useful in recitations, 
reviews, and examinations. The series comprises any section of the world required. 

Monteith's Map-Drawing Scale. 

A ruler of wood, graduated to the ' ' Allen fixed unit of measurement." 



WALL MAPS. 

Monteith's Pictorial Chart of Geography. 

The original drawing for this beautiful and instructive chart was greatly admired in 
the publisher's " exhibit " at the Centennial Exhibition of 1876. It is a picture of the 
earth's surface with every natural feature displayed, teaching also physical geography, 
and especially the mutations of water. The uses to which man puts the earth and its 
treasures and forces, as Agriculture, Mining, Manufacturing, Commerce, and Transpor- 
tation, are also graphically portayed, so that the young learner gets a realistic idea of 
" the world we live in," which weeks of book study might fail to convey. 

Monteith's School Maps, 8 Numbers. 

The "School Series" includes the Hemispheres (2 maps), United States, North 
America, South America, Europe, Asia, Africa. Price, §2.50 each. 

Each map is 28 x 34 inches, beautifully colored, has the names all laid down, and is 
substantially mounted on canvas with rollers. 

Monteith's Grand Maps, 8 Numbers. 

The "Grand Series" includes the Hemispheres (1 map), North America, United 
States, South America, Europe, Asia, Africa, the World on Mercator's Projection, and 
Physical Map of the World. Price, $5.00 each. Size, 42 x 52 inches, names laid down, 
colored, mounted, &c. 

Monteith's Sunday-School Maps. 

Including a map of Paul's Travels ($5.00), one of Ancient Canaan ($3. 00), and Mod- 
ern Palestine ($3.00), or Palestine and Canaan together ($5.00). 

16 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



MATHEMATICS. 



DAVIES'S COMPLETE SERIES, 

ARITHMETIC. 
Davies' Primary Arithmetic. 
Davies' Intellectual Arithmetic. 
Davies' Elements of Written Arithmetic. 
Davies' Practical Arithmetic. 
Davies' University Arithmetic. 

TWO-BOOK SERIES. 

First Book in Arithmetic, Primary and Mental. 
Complete Arithmetic. 

ALGEBRA. 
Davies' New Elementary Algebra. 
Davies' University Algebra. 
Davies' New Bourdon's Algebra. 

GEOMETRY. 
Davies' Elementary Geometry and Trigonometry. 
Davies' Legendre's Geometry. 
Davies' Analytical Geometry and Calculus. 
Davies' Descriptive Geometry. 
Davies' New Calculus. 

MENSURATION. 
Davies' Practical Mathematics and Mensuration. 
Davies' Elements of Surveying. 
Davies' Shades, Shadows, and Perspective. 

MATHEMATICAL SCIENCE. 
Davies' Grammar of Arithmetic. 
Davies' Outlines of Mathematical Science. 
Davies' Nature and Utility of Mathematics. 
Davies' Metric System. 
Davies & Peck's Dictionary of Mathematics. 

17 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

DAVIES'S NATIONAL COURSE 
OF MATHEMATICS. 

ITS RECORD. 

In claiming for this series the first place among American text-books, of whatever 
class, the publishers appeal to the magnificent record which its volumes have earned 
during the thirty-five years of Dr. Charles Davies's mathematical labors. The unremit- 
ting exertions of a life-time have placed the modern series on the same proud eminence 
among competitors that each of its predecessors had successively enjoyed in a course of 
constantly improved editions, now rounded to their perfect fruition, — for it seems 
almost that this science is susceptible of no further demonstration. 

During the period alluded to, many authors and editors in this department have 
started into public notice, and, by borrowing ideas and processes original with Dr. Davies, 
have enjoyed a brief popularity, but are now almost unknown. Many of the series of 
to-day, built upon a similar basis, and described as "modern books," are destined to a 
similar fate ; while the most far-seeing eye will find it difficult to fix the time, on the 
basis of any data afforded by their past history, when these books will cease to increase 
and prosper, and fix a still firmer hold on the affection of every educated American. 

One cause of this unparalleled popularity is found in the fact that the enterprise of the 
author did not cease with the original completion of his books. Always a practical 
teacher, he has incorporated in his text-books from time to time the advantages of every 
improvement in methods of teaching, and every advance in science. During all the 
years in which he has been laboring he constantly submitted his own theories and those 
of others to the practical test of the class-room, approving, rejecting, or modifying 
them as the experience thus obtained might suggest. In this way he has been able 
to produce an almost perfect series of class-books, in which every department of 
mathematics has received minute and exhaustive attention. 

Upon the death of Dr. Davies, which took place in 1876, his work was immediately 
taken up by his former pupil and mathematical associate of many years, Prof. W. G. 
Peck, L.L.D., of Columbia College. By him, with Prof. J. H. Van Amringe, of Columbia 
College, the original series is kept carefully revised and up to the times. 



Davies's System is the acknowledged National Standard foh the United 
States, for the following reasons : — 

1st. It is the basis of instruction in the great national schools at West Point and 
Annapolis. 

2d. It has received the quasi indorsement of the National Congress. 

3d. It is exclusively used in the public schools of the National Capital. 

4th. The officials of the Government use it as authority in all cases involving mathe- 
matical questions. 

5th. Our great soldiers and sailors commanding the national armies and navies were 
educated in this system. So have been a majority of eminent scientists in this country. 
All these refer to "Davies " as authority. 

6th. A larger number of American citizens have received their education from this 
than from any other series. 

7th. The series has a larger circulation throughout the whole country than any other, 
being extensively used in every State in the Union. 

u 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 
DAVIES AND PECK'S ARITHMETICS. 

OPTIONAL OR CONSECUTIVE. 

The best thoughts of these two illustrious mathematicians are combined in the 
following beautiful works, which are the natural successors of Davies's Arithmetics, 
sumptuously printed, and bound in crimson, green, and gold : — 

Davies and Peck's Brief Arithmetic. 

Also called the " Elementary Arithmetic." It is the shortest presentation of the sub- 
ject, and is adequate for all grades in common schools, being a thorough introduction to 
practical life, except for the specialist. 

At first the authors play with the little learner for a few lessons, by object-teaching 
and kindred allurements ; but he soon begins to realize that study is earnest, as he 
becomes familiar with the simpler operations, and is delighted to rind himself master of 
important results. 

The second part reviews the Fundamental Operations on a scale proportioned to 
the enlarged intelligence of the learner. It establishes the General Principles and 
Properties of Numbers, and then proceeds to Fractions. Currency and the Metric 
System are fully treated in connection with Decimals. Compound Numbers and Re- 
duction follow, and finally Percentage with all its varied applications. 

An Index of words and principles concludes the book, for which every scholar and 
most teachers will be gratefid. How much time has been spent in searching for a half- 
forgotten definition or principle in a former lesson ! 

Davies and Peck's Complete Arithmetic. 

This work certainly deserves its name in the best sense. Though complete, it is not, 
like most others which bear the same title, cumbersome. These authors excel in clear, 
lucid demonstrations, teaching the science pure and simple, yet not ignoring convenient 
methods and practical applications. 

For turning out a thorough business man no other work is so well adapted. He will 
have a clear comprehension of the science as a whole, and a working acquaintance 
with details which must serve him well in all emergencies. Distinguishing features of 
the book are the logical progression of the subjects and the great variety of practical 
problems, not puzzles, which are beneath the dignity of educational science. A clear- 
minded critic has said of Dr. Peck's work that it is free from that juggling with 
numbers which some authors falsely call " Analysis." A series of Tables for converting 
ordinary weights and measures into the Metric System appear in the later editions. 



PECK'S ARITHMETICS. 
Peck's First Lessons in Numbers. 

This book begins with pictorial illustrations, and unfolds gradually the science of 
numbers. It noticeably simplifies the subject by developing the principles of addition 
and subtraction simultaneously ; as it does, also, those of multiplication and division. 

Peck's Manual of Arithmetic. 

This book is designed especially for those who seek sufficient instruction to carry 
them successfully through practical life, but have not time for extended study. 

Peck's Complete Arithmetic. 

This completes the series but is a much briefer book than most of the complete 
arithmetics, and is recommended not only for what it contains, but also for what is 
omitted. 

It maybe said of Dr. Peck's books more truly than of any other series published, that 
they are clear and simple in definition and rule, and that superfluous matter of every 
kind has beer, faithfully eliminated, thus magnifying the working value of the book 
and saving unnecessary expense of time and labor. 

19 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



BARNES'S NEW MATHEMATICS. 

In this series Joseph Ficklin, Ph. D., Professor of Mathematics and Astronomy 
in the University of Missouri, lias combined all the best and latest results of practical 
and experimental teaching of arithmetic with the assistance of many distinguished 
mathematical authors. 



Barnes's Elementary Arithmetic. 
Barnes's National Arithmetic. 

These two works constitute a complete arithmetical course in tvjo looks. 

They meet the demand for text-books that will help students to acquire the greatest 
amount of useful and practical knowledge of Arithmetic by the smallest expenditure of 
time, labor, and money. Nearly every topic in Written Arithmetic is introduced, and its 
principles illustrated, by exercises in Oral Arithmetic. The free use of Equations ; the 
concise method of combining and treating Properties of Numbers; the treatment of 
Multiplication and Division of Fractions in two cases, and then reduced to one; Can- 
cellation by the use of the vertical line, especially in Fractions, Interest, and Proportion ; 
the brief, simple, and greatly superior method of working Partial Payments by the 
" Time Table " and Cancellation ; the substitution of formulas to a great extent for 
rules ; the full and practical treatment of the Metric System, &c, indicate their com- 
pleteness. A variety of methods and processes for the same topic, which deprive the 
pupil of the great benefit of doing a part of the thinking and labor for himself, have 
been discarded. The statement of principles, definitions, rules, &o, is brief and simple. 
The illustrations and methods are explicit, direct, and practical. The great number 
and variety of Examples embody the actual business of the day. The very large 
amount of matter condensed in so small a compass has been accomplished by econo- 
mizing every line of space, by rejecting superfluous matter and obsolete terms, and by 
avoiding the repetition of analyses, explanations, and operations in the advanced topics 
which have been used in the more elementary parts of these books. 

AUXILIARIES. 

For use in district schools, and for supplying a text-book in advanced work for 
classes having finished the course as given in the ordinary Practical Arithmetics, the 
National Arithmetic has been divided and bound separately, as follows : — 

Barnes's Practical Arithmetic. 

Barnes's Advanced Arithmetic. 

In many schools there are classes that for various reasons never reach beyond 
Percentage. It is just such cases where Barnes's Practical Arithmetic will answer a 
good purpose, at a price to the pupil much less than to buy the complete book. On the 
other hand, classes having finished the ordinary Practical Arithmetic can proceed 
with the higher course by using Barnes's Advanced Arithmetic. 

For primary schools requiring simply a table book, and the earliest rudiments 
forcibly presented through object-teaching and copious illustrations, we have 
prepared 

Barnes's First Lessons in Arithmetic, 

which begins with the most elementary notions of numbers, and proceeds, by simple 
steps, to develop all the fundamental principles of Arithmetic. 



Barnes's Elements of Algebra. 

This work, as its title indicates, is elementary in its character and suitable for use, 
(1) in such public schools as give instruction in the Elements of Algebra ; (2) in institu- 
tions of learning whose courses of study- do not include Higher Algebra ; (3) in schools 
whose object is to prepare students for entrance into our colleges and universities. 
This book will also meet the wants of students of Physics who require some knowledge of 

20 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



Algebra. The student's progress in Algebra depends very largely upon the proper treat- 
ment of the four Fundamental Operations. The terms Addition, Subtraction, Multiplication, 
and Division in Algebra have a wider meaning than in Arithmetic, and these operations 
have been so defined as to include their arithmetical meaning ; so that the beginner 
is simply called upon to enlarge his views of those fundamental operations. Much 
attention has been given to the explanation of the negative sign, in order to remove the 
well-known difficulties in the use and interpretation of that sign. Special attention is 
here called to " A Short Method of Removing Symbols of Aggregation," Art, 76. On 
account of their importance, the subjects of Factoring, Greatest Common Divisor, and 
Least Common Multiple have been treated at greater length than is usual in elementary 
works. In the treatment of Fractions, a method is used which,is quite simple, and, 
at the same time, more general than that usually employed. In connection with Radical 
Quantities the roots are expressed by fractional exponents, for the principles and rules 
applicable to integral exponents may then be used without modification. The Equation 
is made the chief subject of thought in this work. It is defined near the beginning, 
and used extensively in every chapter. In addition to this, four chapters are devoted 
exclusively to the subject of Equations. All Proportions are equations, and in their 
treatment as such all the difficulty commonly connected with the subject of Proportion 
disappears. The chapter on Logarithms will doubtless be acceptable to many teachers 
who do not require the student to master Higher Algebra before entering upon the 
study of Trigonometry. 



HIGHER MATHEMATICS. 
Peck's Manual of Algebra. 

Bringing the methods of Bourdon within the range of the Academic Course. 

Peck's Manual of Geometry. 

By a method purely practical, and unembarrassed by the details which rather confuse 
than simplify science. 

Peck's Practical Calculus. 
Peck's Analytical Geometry. 
Peck's Elementary Mechanics. 
Peck's Mechanics, with Calculus. 

The briefest treatises on these subjects now published. Adopted by the great Univer- 
sities : Yale, Harvard, Columbia, Princeton, Cornell, &c. 

Macnie's Algebraical Equations. 

Serving as a complement to the more advanced treatises on Algebra, giving special 
attention to the analysis and solution of equations with numerical coefficients. 

Church's Elements of Calculus. 

Church's Analytical Geometry. 

Church's Descriptive Geometry. With plates. 2 vols. 

These volumes constitute the " West Point Course " in their several departments. 
Prof. Church was long the eminent professor of mathematics at West Point Military 
Academy, and his works are standard in all the leading colleges. 

Courtenay's Elements of Calculus. 

A standard work of the very highest grade, presenting the most elaborate attainable 
survey of the subject. 

Hackley's Trigonometry. 

With applications to Navigation and Surveying, Nautical and Practical Geometry, 
and Geodesy. 

21 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 




GENERAL HISTORY. 

Monteith's Youth's History of the United States. 

A History of the United States for beginners. It is arranged upon the catechetical plan, 
with illustrative maps and engravings, review questions, dates in parentheses (that their 
study may be optional with the younger class of learners), and interesting biographical 
sketches of all persons who have been prominently identified with the history of our 
country. 

Willard's United States. School and University Editions. 

The plan of this standard work is chronologically exhibited in front of the titlepage. 
The maps and sketches are" found useful assistants to the memory ; and dates, usually 
so difficult to remember, are so systematically arranged as in a great degree to obviate 
the difficulty. Candor, impartiality, and accuracy are the distinguishing features of 
the narrative portion. 

Willard's Universal History. New Edition. 

The most valuable features of the ' ; United States " are reproduced in this. The 
peculiarities of the work are its great conciseness and the prominence given to the 
chronological order of events. The margin marks each successive era with great dis- 
tinctness, so that the pupil retains not only the event but its time, and thus fixes the 
order of history firmly and usefully in his mind. Mrs. Willard's books are constantly 
revised, and at all times written up to embrace important historical events of recent 
date. Professor Arthur Gilman has edited the last twenty-five years to 1882. 

Lancaster's English History. 

By the Master of the Stoughton Grammar School, Boston. The most practical of the 
"brief books." Though short, it is not a bare and uninteresting outline, but contains 
enough of explanation and detai 1 to make intelligible the cause and effect of events. 
Their relations to the history and development of the American people is made specially 
prominent. 

Willis's Historical Reader. 

Being Collier's Great Events of History adapted to American schools. This rare 
epitome of general history, remarkable for its charming style and judicious selection of 
events on which the destinies of nations have turned, has been skilfully manipulated 
by Professor Willis, with as few changes as would bring the United States into its proper 
position in the historical perspective. As reader or text-book it has few equals and no 
superior. 

Berard's History of England. 

By an authoress well known for the success of her History of the United States. 
The social life of the English people is felicitously interwoven, as in fact, with the civil 
and military transactions of the realm. 

Ricord's History of Rome. 

Possesses the charm of an attractive romance. The fables with which this history 
abounds are introduced in such a way as not to deceive the inexperienced, while adding 
materially to the value of the work as a reliable index to the character and institutions, 
as well as the history of the Roman people. 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

HISTORY — Continued. 

Hanna's Bible History. 

The only compendium of Bible narrative which affords a connected and chronological 
view of the important events there recorded, divested of all superfluous detail. 

Summary of History ; American, French, and English. 

A well-proportioned outline of leading events, condensing the substance of the more 
sxtensive text-books in common use into a series of statements so brief, that every 
word may be committed to memory, and yet so comprehensive that it presents an 
accurate though general view of the whole continuous life of nations. 

Marsh's Ecclesiastical History. 

Affording the History of the Church in all ages, with accounts of the pagan world 
during thebiblieal periods, and the character, rise, and progress of all religions, as well 
as the various sects of the worshippers of Christ. The work is entirely non-sectarian, 
though strictly catholic. A separate volume contains carefully prepared questions for 
class use. 

Mill's History of the Ancient Hebrews. 

With valuable Chronological Charts, prepared by Professor Edwards of N. Y. This 
is a succinct account of the chosen people of God to the time of the destruction of 
Jerusalem. Complete in one volume. 

Topical History Chart Book. 

By Miss Ida P. Whitcomb. To be used in connection with any History, Ancient or 
Modern, instead of the ordinary blank book for summary. It embodies the names of 
contemporary rulers from the earliest to the present time, with blanks under each, in 
which the pupil may write the summary of the life of the ruler. 

Gilman's First Steps in General History. 

A "suggestive outline" of rare compactness. Each country is treated by itself, and 
the United States receive special attention. Frequent maps', contemporary events in 
tables, references to standard works for fuller details, and a minute Index constitute 
the " Illustrative Apparatus." From no other work that we know of can so succinct a 
view of the world's history be obtained. Considering the necessary limitation of space, 
the style is surprisingly vivid, and at times even ornate. In all respects a charming, 
though not the less practical, text-book. 

Baker's Brief History of Texas. 
Dimitry's History of Louisana. 
Alison's Napoleon First. 

The history of Europe from 17SS to 1815. By Archibald Alison. Abridged by Edward 
S. Gould. One vol., Svo, with appendix, questions, and maps. 550 pages. 

Lord's Points of History. 

The salient points in the history of the world arranged catechetically for class use or 
for review and examination of teacher or pupil. By John Lord LL D 12mo 300 
pages. . ' 

Carrington's Battle Maps and Charts of the American 
Revolution. 

Topographical Maps and Chronological Charts of every battle, with 3 steel portraits 
of ^Yashmgton. Svo, cloth. 

Condit's History of the English Bible. 

For theological and historical students this book has an intrinsic value. It gives the 
history of all the English translations down to the present time, together with a careful 
review of their influence upon English literature and language. 

23 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



BARNES'S ONE-TERM HISTORY 
SERIES. 

A taSf'ipIS'lSf IE 




A Brief History of the United 
States. 

This is probably the most original school-book pub- 
lished for many, years, in any department. A few of its 
claims are the following : — 

i . Brevity. — The text is complete for grammar school 
or intermediate classes, in 290 12mo pages, large type. 
It may readily be completed, if desired, in one term of 
study. 

2. Comprehensiveness. — Though so brief, this book 
contains the pith of all the wearying contents of the larger 
manuals, and a great deal more than the memory usually 
retains from the latter. 

3. Interest has been a prime consideration. Small 
books have heretofore been bare, full of dry statistics, unattractive. This one is 
charmingly written, replete with anecdote, and brilliant with illustration. 

4. Proportion of Events. — It is remarkable for the discrimination with which 
the different portions, of our history are presented according to their importance. Thus 
the older works, being already large books when the Civil War took place, give it less 
space than that accorded to the Revolution. 

5. Arrangement. — In six epochs, entitled respectively, Discovery and Settlement, 
the Colonies, the Eevolntion, Growth of States, the Civil War, and Current Events. 

6. Catch Words. — Each paragraph is preceded by its leading thought in promi- 
nent type, standing in the student's mind for the whole paragraph. 

7. Key Notes. — Analogous with this is the idea of grouping battles, &c, about 
some central event, which relieves the sameness so common in such descriptions, and 
renders each distinct by some striking peculiarity of its own. 

8. Foot-Notes. — these are crowded with interesting matter that is not strictly a 
part of history proper. They may be learned or not, at pleasure. They are certain 
in any event to be read. 

9. Biographies of all the leading characters are given in full in foot-notes. 

10. Maps. — Elegant and distinct maps from engravings on copper-plate, and beauti- 
fully colored, precede each epoch, and contain all the places named. 

u. Questions are at the back of the book, to compel a more independent use of the 
text. Both text and questions are so worded that the pupil must give intelligent 
answers in his own words. " Yes " and " No " will not do. 



24 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



HISTORY — Continued. 

12 Historical Recreations. — These are additional questions to test the student's 
knowledge in review, as: "What trees are celebrated in our history?" "When 
did a fo° 'save our army?" "What Presidents died in office?" "When was the 
Mississippi our western boundary?" "Who said, 'I would rather be right than 
President ' ? " &c. 

13 The Illustrations, about seventy in number, are the work of our best artists 
and engravers, produced at great expense. They are vivid and interesting, and mostly 
upon subjects never before illustrated in a school-book. 

14 Dates- — Only the leading dates are given in the text, and these are so associated 
as to assist the memory, but at the head of each page is the date of the event first 
mentioned and at the close of each epoch a summary of events and dates. 

15. The Philosophy of History is studiously exhibited, the causes and effects 
of events being distinctly traced and their inter-connection shown. 

16. Impartiality. — All sectional, partisan, or denominational views are avoided. 
Facts are stated after a careful comparison of all authorities without the least prejudice 
or favor. ' 

17. Index. — A verbal index at the close of the book perfects it as a work of reference. 
It will be observed that the above are all particulars in which School Histories have 

been signally defective, or altogether wanting. Many other claims to favor it shares in 
common with its predecessors. 



TESTIMONIALS. 



From Prof. Wm. F. Allen, State Uni- 
versity of Wisconsin. 

"Two features that I like very much 
are the anecdotes at the foot of the page 
and the 'Historical Recreations' in the 
Appendix. The latter, I think, is quite 
a new feature, and the other is very well 
executed." 

From Hon. Newton Bateman, Superin- 
tendent Public Instruction, Illinois. 

"Barnes's One-Term History of the 
United States is an exceedingly attrac- 
tive and spirited little book. Its claim 
to several new and valuable features seems 
well founded. Under the form of six well- 
defined epochs, the history of the United 
States is traced tersely, yet pithily, from 
the earliest times to the present day. A 
good map precedes each epocdi, whereby 
the history and geography of the period 
may be studied together, as thnj always 
should be. The syllabus of each paragraph 
is made to stand in such bold relief, by 
the use of large, heavy type, as to be of 
much mnemonic value to the student. The 
book is written in a sprightly and pi- 
quant style, the interest never flagging 
from beginning to end, — a rare and diffi- 
cult achievement in works of this kind." 

From Hon. Abner J. Phipps, Superin- 
tendent Schools, Leu-is ton, Maine. 
" Barnes's History of the United States 



has been used for several years in the 
Lewiston schools, and has proved a very 
satisfactory work. I have examined the 
new edition of it." 

From Hon. R. K. Buchell, City Superin- 
tendent Schools, Lancaster, Pa. 
" It is the best history of the kind I have 
ever seen." 

From T. J. Charlton, Superintendent 
Pv.hlic Schools, Vincennes, hid. 
"We have used it here for six years, 
and it has given almost perfect satisfac- 
tion. . . . The notes in fine print at the 
bottom of the pages are of especial value." 

From Prof. Wm. A. Mowey, E. #• C. 
School, Providence, R. I. 

" Permit me to express my high appre- 
ciation of your book. I wish all text- 
books for the young had equal merit." 

From Hon. A. M. Keiley, City Attorney, 
Late Mayor, and President of the School 
Board, City of Richmond, Va. 
" I do not hesitate to volunteer to you 
the opinion that Barnes 's History is en- 
titled to the preference in almost every 
respect that distinguishes a good school- 
book. . . . The narrative generally exhibits 
the temper of the judge ; rarely, if ever, 
of the advocate." 



2o 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



HRiSfjuwfl 




Brief History of An- 
cient Peoples. 

With an account of their monuments 
literature, and manners. 340 S 
12mo Profusely illustrated l g S ' 
„£> wo . rk the Political history 
which occupies nearly, if not a J 
the ordinary school text, is condensed 
to the salient and essential facts In 
order to give room for a clear outline 
of the literature, religion, architect,^ 
character, habits, &c., of eac „2 
Surely it is as important to know some- 
thing -about Plato as aM about Caesar 
and to learn how the ancients wrote 
oatSes ^ h ° Wthey *«*« *S 

The chapters on Manners and Cus- 
toms and the Scenes in Real Life rerrt 
^~-<\ sent the people of history as men and 
and fear S as ourselves, and so brin- the «K«w rll men S ? bject tothe same w a«ts, hopes 
intended »fy/ or reading, are the "result of »1 ?f K*? 1 to us - The Sc enes, wh eh are 
H^W" the L ° n ^ n nS&^-^?^ collects S 
of the latest authorities on the domestic S'^ 1 ? 1118 ," 1 Rome and Pompeii, and 
written in a semi-romantic style tTev are Snl/l "-^ pe °P les - Thon S h intentionally 

SL5 me of them are ^fiSrfft 

alabaster or pamted on Egyptian walls. P the details scul Ptured in Assyrian 

26 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



HISTORY — Continued. 

The extracts made from the sacred books of the East are not specimens of their style 
and teachings, but only gems selected often from a mass of matter, much of which would 
be absurd, meaningless, and even revolting. It has not seemed best to cumber a book 
like this with selections conveying no moral lesson. 

The numerous cross-references, the abundant dates in parenthesis, the pronunciation 
of the names in the Index, the choice readiug references at the (dose of each general 
subject, and the novel Historical Recreations in the Appendix, will be of service to 
teacher and pupil alike. 

Though designed primarily for a text-book, a large class of persons — general readers, 
who desire to know something about the progress of historic criticism and Jae recent 
discoveries made among the resurrected monuments of the East, but have no leisure to 
read the ponderous volumes of Brugsch, Layard, Grote, Mommsen, and Ihne — will find 
this volume just what they need. 



From Homer B. Sprague, Heal Master 
Girls' High School, West Newton St., Bos- 
to?i, Mass. 
" I beg to recommend in strong terms 

the adoption of Barnes's 'History of 



Ancient Peoples' as a text-book. It is 
about as nearly perfect as could be 
hoped for. The adoption would give 
great relish to the study of Ancient 
History." 



jst H1STO1 




HE Brief History of France. 

By the author of the " Brnf United States," 
with all the attractive features of that popu- 
lar work (which see) and new ones of its own. 

It is believed that the History of France 
has never before been presented in such 
brief compass, and this is effected without 
sacrificing one particle of interest. The book 
reads like a romance, and, while drawing the 
student by an irresistible fascination to his 
task, impresses the great outlines indelibly upon the memory. «- 

27 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



DRAWING. 

BARNES'S POPULAR DRAWING SERIES. 

Based upon the experience of the most successful teachers of drawing in the United 
States. 

The Primary Course, consisting of a manual, ten cards, and three primary 
drawing books, A, B, and 0. 

Intermediate Course. Four numbers and a manual. 

Advanced Course. Four numbers and a manual. 

Instrumental Course. Four numbers and a manual. 

The Intermediate, Advanced, and Instrumental Courses are furnished either in book 
or card form at the same prices. The books contain the usual blanks, with the unusual 
advantage of opening from the pupil, — placing the copy directly in front and above 
the blank, thus occupying but little desk-room. The cards are in the end more econom- 
ical than the books, if used in connection with the patent blank folios that accompany 
this series. 

The cards are arranged to be bound (or tied) in the folios and removed at pleasure. 
The pupil at the end of each number has a complete book, containing only his own 
work, while the copies are preserved and inserted in another folio ready for use in the 
next class. 

Patent Blank Folios. No. 1. Adapted to Intermediate Course. No. 2. Adapted 
to Advanced and Instrumental Courses. 

ADVANTAGES OF THIS SERIES. 

The Plan and Arrangement. — The examples are so arranged that teachers and 
pupils can see, at a glance, how they are to be treated and where they are to be copied. 
In this system, copying and designing do not receive all the attention. The plan is 
broader in its aims, dealing with drawing as a branch of common-school instruction, 
and giving it a wide educational value. 

Correct Methods. — In this system the pupil is led to rely upon himself, and not 
upon delusive mechanical aids, as printed guide-marks, &c. 

One of the principal objects of any good course in freehand drawing is to educate the 
eye to estimate location, form, and size. A system which weakens the motive or re- 
moves the necessity of thinking is false in theory and ruinous in practice. The object 
should be to educate, not cram ; to develop the intelligence, not teach tricks. 

Artistic Effect- — The beauty of the examples is not destroyed by crowding the 
pages with useless and badly printed text. The Manuals contain all necessary 
instruction. 

Stages of Development. —Many of the examples are accompanied by diagrams, 
showing the different stages of development. 

Lithographed Examples. — The examples are printed in imitation of pencil 
drawing (not in hard, black lines) that the pupil's work may resemble them. 

One Term's Work. — Each book contains what can be accomplished in an average 
term, and no more. Thus a pupil finishes one book before beginning another. 

Quality — not Quantity. — Success in drawing depends upon the amount of thought 
exercised by the pupil, and not upon the large number of examples drawn. 

Designing. ->— Elementary design is more skilfully taught in this system than by 
any other, in addition to the instruction given in the books, the pupil will tind printed 
on the insides of the covers a variety of beautiful patterns. 

Enlargement and Reduction. — The practice of enlarging and reducing from 
copies is not commenced until the pupil is well advanced in the course and therefore 
better able to cope with this difficult feature in drawing. 

Natural Forms. —This is the only course that gives at convenient intervals easy 
and progressive exercises in the drawing of natural forms. 

Economy. — By the patent binding described above, the copies need not be thrown 
aside when a book is filled out, but are preserved in perfect condition for future use. 
The blank books, only, will have to be purchased after the first introduction, thus effect- 
ing a saving of more than half in the usual cost of drawing-books. 

Manuals for Teachers. — The Manuals accompanying this series contain practical 
instructions for conducting drawing in the class-room, with definite directions for draw- 
ing each of the examples in the books, instructions for designing, model and object 
drawing, drawing from natural forms, &c. 

28 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

DRAWING — Continued. 

Chapman's American Drawing-Book. 

The standard American text-book and authority in all branches of art. A compilation 
of art principles. A manual for the amateur, and basis of study for the professional 
artist. Adapted for schools and private instruction. 

Contents. — " Any one who can Learn to Write can Learn to Draw." — Primary In- 
struction in Drawing. — Rudiments of Drawing the Human ' Head. — Rudiments in 
Drawing the Human Figure. — Rudiments of Drawing. — The Elements of Geometry. — 
Perspective. — Of Studying and Sketching from Nature. — Of Painting. — Etching and 
Engraving. — Of Modelling. — Of Composition. — Advice to the American Art-Student. 

The work is of course magnificently illustrated with all the original designs. 

Chapman's Elementary Drawing-Book. 

A progressive course of practical exercises, or a text-book for the training of the 
eye and hand. It contains the elements from the larger work, and a copy should be in 
the hands of every pupil ; while a copy of the " American Drawing-Book," named above, 
should be at hand for reference by the class. 

Clark's Elements of Drawing. 

A complete course in this graceful art, from the first rudiments of outline to the 
finished sketches of landscape and scenery. 

Allen's Map-Drawing and Scale. 

This method introduces a new era in map-drawing, for the following reasons : 1. It 
is a system. This is its- greatest merit. — 2. It is easily understood and taught. — 
3. The eye is trained to exact measurement by the use of a scale. — 4. By no special 
effort of the memory, distance and comparative size are fixed in the mind. — 5. It dis- 
cards useless construction of lines. — 6. It can be taught by any teacher, even though 
there may have been no previous practice in map-drawing. — 7. Any pupil old enough 
to study geography can learn by this system, in a short time, to draw accurate maps. 
— 8. The system is not the result of theory, but comes directly from the school-room. 
It has been thoroughly and successfully tested there, with all grades of pupils. — 9. It 
is economical, as it requires no mapping plates. It gives the pupil the ability of rapidly 
drawing accurate maps. 

FINE ARTS. 

Hamerton's Art Essays (Atlas Series) : — 

No. 1. The Practical "Work of Painting. 
With portrait of Rubens. Svo. Paper covers. 

No. 2. Modern Schools of Art- 
Including American, English, and Continental Painting. Svo. Paper covers. 

Huntington's Manual of the Fine Arts. 

A careful manual of instruction in the history of art, up to the present time. 

Boyd's Karnes' Elements of Criticism. 

The best edition of the best work on art and literary criticism ever produced in 
English. 

Benedict's Tour Through Europe. 

A valuable companion for any one wishing to visit the galleries and sights of the 
continent of Europe, as well as a charming book of travels. 

Dwight's Mythology. 

A knowledge of mythology is necessary to an appreciation of ancient art. 

Walker's World's Fair. 

The industrial and artistic display at the Centennial Exhibition. 

29 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 




Design from Chapman's Drawing-Book. 



30 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

BOOK-KEEPING TEXT. 

Powers's Practical Book-keeping. 
Powers's Blanks to Practical Book-keeping. 

A Treatise on Book-keeping, for Public Schools and Academies. By Millard R. 
Powers, M. A. This work is designed to impart instruction upon the science of accounts, 
as applied to mercantile business, and it is believed that more knowledge, and that, too, 
of a more practical nature, can be gained by the plan introduced in this work, than by 
any other published. 

Folsom's Logical Book-keeping. 
Folsom's Blanks to Book-keeping. 

This treatise embraces the interesting and important discoveries of Professor Folsom (of 
the Albany " Bryant & Stratton College "), the partial enunciation of which in lectures 
and otherwise lias attracted so much attention in circles interested in commercial 
education. 

After studying business phenomena for many years, he has arrived at the positive 
laws and principles that underlie the whole subject of accounts ; finds that the science 
is based in value as a generic term ; that value divides into two classes with varied 
species ; that all the exchanges of values are reducible to nine equations ; and that all 
the results of all these exchanges are limited to thirteen in number. 

As accounts have been universally taught hitherto, without setting out from a radical 
analysis or definition of values, the science has been kex>t in great obscurity, and been 
made as difficult to impart as to acquire. On the new theory, however, these obstacles 
are chiefly removed. In reading over the first part of it, in which the governing laws 
and principles arc discussed, a person with ordinary intelligence will obtain a fair con- 
ception of the double-entry process of accounts. But when he comes to study thoroughly 
these laws and principles as there enunciated, and works out the examples and memo- 
randa which elucidate the thirteen results of business, the student will neither fail in 
readily acquiring the science as it is, nor in becoming able intelligently to apply it in 
the interpretaiion of business 

Smith and Martin's Book-keeping. 
Smith and Martin's Blanks. 

This wor.i is by a practical teacher and a practical book-keeper. It is of a thoroughly 
popular class, and will be welcomed by every one who loves to see theory and practice 
combined in an easy, concise, and methodical form. 

The single-entry portion is well adapted to supply a want felt in nearly all other 
treatises, which seem to be prepared mainly for the use of wholesale merchants ; 
leaving retailers, mechanics, farmers, &c. , who transact the greater portion of the 
business of the country, without a guide. The work is also commended, on this 
account, for general use in young ladies' seminaries, where a thorough grounding 
in the simpler form of accounts will be invaluable to the future housekeepers of the 
nation. 

The treatise on double-entry book-keeping combines all the advantages of the 
most recent methods with the utmost simplicity of application, thus affording the 
pupil all the advantages of actual experience in the counting-house, and giving a 
clear comprehension of the entire subject through a judicious course of mercantile 
transactions. 



PRACTICAL BOOK-KEEPING. 

Stone's Post-Office Account Book. 

By Micah H. Stone. For record of Box Rents and Postages. Three sizes always in 
stock. 64, 10S, and 204 pages. 

INTEREST TABLES. 

Brooks's Circular Interest Tables. 

To calculate simple and compound interest for any amount, from 1 cent to $1,000, at 
current rates from 1 day to 7 years. 

31 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

DR. STEELE'S ONE-TERM SERIES, 
IN ALL THE SCIENCES. 

Steele's 14-Weeks Course in Chemistry. 
Steele's 14-Weeks Course in Astronomy. 
Steele's 14-Weeks Course in Physics. 
Steele's 14-Weeks Course in Geology. 
Steele's 14-Weeks Course in Physiology. 
Steele's 14-Weeks Course in Zoology. 
Steele's 14-Weeks Course in Botany. 

Our text-books in these studies are, as a general thing, dull and uninteresting. 
They contain from 400 to 600 pages of dry facts and unconnected details. They abound 
in that which the student cannot learn, much less remember. The pupil commences 
the study, is confused by the fine print and coarse print, and neither knowing exactly 
what to learn nor what to hasten over, is crowded through the single term generally 
assigned to each branch, and frequently comes to the close without a definite and exact 
idea of a single scientific principle. 

Steele's " Fourteen- Weeks Courses " contain only that which every well-informed per- 
son should know, while all that which concerns only the professional scientist is omitted. 
The language is clear, simple, and interesting, and the illustrations bring the subject 
within the range of home life and daily experience. They give such of the general 
principles and the prominent facts as a pupil can make familiar as household words 
within a single term. The type is large and open ; there is no fine print to annoy ; 
the cuts are copies of genuine experiments or natural phenomena, and are of fine 
execution. 

In fine, by a system of condensation peculiarly his own, the author reduces each 
branch to the limits of a single term of study, while sacrificing nothing that is essential, 
and nothing that is usually retained from the study of the larger manuals in common 
use. Thus the student has rare opportunity to economize his time, or rather to employ 
that which he has to the best advantage. 

A notable feature is the author's charming "style," fortified by an enthusiasm over 
his subject in which the student will not fail to partake. Believing that Natural 
Science is full of fascination, he has moulded it into a form that attracts the attention 
and kindles the enthusiasm of the pupil. 

The recent editions contain the author's " Practical Questions " on a plan never 
before attempted in scientific text-books. These are questions as to the nature and 
cause of common phenomena, and are not directly answered in the text, the design 
being to test and promote an intelligent use of the student's knowledge of the foregoing 
principles. 

Steele's Key to all His Works. 

This work is mainly composed of answers to the PracticalQuestions, and solutions of the 
problems, in the author's celebrated " Fourteen-Weeks Courses " in the several sciences, 
with many hints to teachers, minor tables, &c. Should be on every teacher's desk. 

Prof. J. Dorman Steele is an indefatigable student, as well as author, and his books 
have reached a fabulous circulation. It is safe to say of his books that they have 
accomplished more tangible and better results in the class-room than any other ever 
offered to American schools, and have been translated into more languages for foreign 
schools. They are even produced in raised type for the blind. 

32 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



THE NEW GANOT. 

Introductory Course of Natural Philosophy. 

This book was originally edited from Ganot's " Popular Physics," by William G. 
Peck, LL.D., Professor of Mathematics and Astronomy, Columbia College, and of 
Mechanics in the School of Mines. It has recently been revised by Levi S. Bur- 
bank, A. M., late Principal of Warren Academy, Woburn, Mass., and James I. Hanson, 
A.M., Principal of the High School, Woburn, Mass. 

Of elementary works those of M. Ganot stand pre-eminent, not only as popular 
treatises, but as thoroughly scientific expositions of the principles of Physics. His 
" Traite de Physique " has not only met with unprecedented success in France, but has 
been extensively used in the preparation of the best works on Physics that have been 
issued from the American press. 

In addition to the "Traite de Physique," which is intended for the use of colleges 
and higher institutions of learning, M. Ganot published this more elementary work, 
adapted to the use of schools and academies, in which he faithfully preserved the 
prominent features and all the scientific accuracy of the larger work. It is charcter- 
ized by a well-balanced distribution of subjects, a logical development of scientific 
principles, and a remarkable clearness of definition and explanation. In addition, it is 
profusely illustrated with beautifully executed engravings, admirably calculated to 
convey to the mind of the student a clear conception of the principles unfolded. Their 
completeness and accuracy are such as to enable the teacher to dispense with much of 
the apparatus usually employed in teaching the elements of Physical Science. 

After several years of great popularity the American publishers have brought this 
important book thoroughly up to the times. The death of the accomplished educator, 
Professor Burbank, took place before he had completed his work, and it was then 
taken in hand by his friend, Professor Hanson, who was familiar with his plans, and 
has ably and satisfactorily brought the work to completion. 

The essential characteristics and general plan of the book have, so far as possible, 
been retained, but at the same time many parts have been entirely rewritten, much 
new matter added, a large number of new cuts introduced, and the whole treatise 
thoroughly revised and brought into harmony with the present advanced stage of sci- 
entific discovery. 

Among the new features designed to aid in teaching the subject-matter are the 
summaries of topics, which, it is thought, will be found very convenient in short 
reviews. 

As many teachers prefer to prepare their own questions on the text, and many do not 
have time to spend in the solution of problems, it has been deemed expedient to insert 
both the review questions and problems at the end of the volume, to be used or not at 
the discretion of the instructor. 



Fram the Churchman. 

" No department of science has under- 
gone so many improvements and changes 
in the last quarter of a century as that of 
natural philosophy. So many and so im- 
portant have been the discoveries and 
inventions in every branch of it that 
everything seems changed but its funda- 
mental principles. Ganot has chapter 
upon chapter upon subjects that were not 
so much as known by name to Olmsted ; 
and here we have Ganot, first edited by 
Professor Peck, and afterward revised by 
the late Mr. Burbank and Mr. Hanson. No 
elementary works upon philosophy have 
been superior to those of Ganot, either as 
popular treatises or as scientific exposi- 
tions of the principles of physics, and 
his ' Traite de Physique ' has not only had 
a great success in France, but has been 
freely used in this country in the prepa- 
ration of American books upon the sub- 



jects of which it treats. That work was 
intended for higher institutions of learn- 
ing, and Mr. Ganot prepared a more 
elementary work for schools and acade- 
mies. It is as scientifically accurate as 
the larger work, and is characterized by 
a logical development of scientific princi- 
ples, by clearness of definition and expla- 
nation, by a proper distribution of sub- 
jects, and by its admirable engravings. 
We here have Ganot's work enhanced in 
value by the labors of Professor Peck and of 
Messrs. Burbank and Hanson, and brought 
up to our own times. The essential char- 
acteristics of Ganot's work haA r e been re- 
tained, but much of the book has been 
rewritten, and many new cuts have been 
introduced, made necessary by the prog- 
ress of scientific discovery. The short 
reviews, the questions on the text, and 
the problems given for solution are desir- 
able additions to a work of this kind, and 
will give the book increased popularity. " 



34 




[Specimen Illustration from Steele's Sciences.] 

35 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS, 



FAMILIAR SCIENCE. 

Norton & Porter's First Book of Science. 

Sets forth the principles of Natural Philosophy, Astronomy, Chemistry, Physiology, 
and Geology, on the catechetical plan for primary classes and beginners. 

Chambers's Treasury of Knowledge. 

Progressive lessons upon — first, common things which lie most immediately around 
us, and first attract the attention of the young mind ; second, common objects from the 
mineral, animal, and vegetable kingdoms, manufactured articles, and miscellaneous 
substances ; third, a systematic view of nature under the various sciences. May be 
used as a reader or text-book. 

Monteith's Easy Lessons in Popular Science. 

This book combines within its covers more attractive features for the study of science 
by children than any other book published. It is a reading book, spelling book, com- 
position book, drawing book, geography, history, book on botany, zoology, agricul- 
ture, manufactures, commerce, and natural philosophy. All these subjects are presented 
in a simple and effective style, such as would be adopted by a good teacher on an 
excursion with a class. The class are supposed to be taking excursions, with the help 
of a large pictorial chart of geography, which can be suspended before them in the 
school-room. A key of the chart is inserted in every copy of the book. With this 
book the science of common or familiar things can be taught to beginners. 



NATURAL PHILOSOPHY. 

Norton's First Book in Natural Philosophy. 
Peck's Elements of Mechanics. 

A suitable introduction to Bartlett's higher treatises on Mechanical Philosophy, and 
adequate in itself for a complete academical course. 

Bartlett's Analytical Mechanics. 
Bartlett's Acoustics and Optics. 

A complete system of Collegiate Philosophy, by Prof. W. H. C. Bartlett, of West 
Point Military Academy. 

Steele's Physics. 

Peck's Ganot. 

GEOLOGY. 

Page's Elements of Geology. 

A volume of Chambers's Educational Course. Practical, simple, an* 1 p.minently 
calculated to make the study interesting. 

Steele's Geology. 

CHEMISTRY. 

Porter's First Book of Chemistry. 
Porter's Principles of Chemistry. 

The above are widely known as the productions of one of the most eminent scientific 
men of America. The extreme simplicity in the method of presenting the science, while 
exhaustively treated, has excited universal commendation. 

Gregory's Chemistry (Organic and Inorganic). 2 vols. 

The science exhaustively treated. For colleges and medical students. 

Steele's Chemistry. 

36 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

NATURAL SCIENCE — Continued. 

BOTANY. 

Wood's Object-Lessons in Botany. 
Wood's American Botanist and Florist. 
Wood's New Class-Book of Botany. 

The standard text-books of the United States in this department. In style they are 
simple, popular, and lively ; in arrangement, easy and natural ; in description, graphic 
and scientific. The Tables for Analysis are reduced to a perfect system. They include 
the flora of the whole United States east of the Rocky Mountains, and are well adapted 
to the regions west. 

Wood's Descriptive Botany. 

A complete flora of all plants growing east of the Mississippi River. 

Wood's Illustrated Plant Record. 

A simple form of blanks for recording observations in the field. 

Wood's Botanical Apparatus. 

A portable trunk, containing drying press, knife, trowel, microscope, and tweezers, 
and a copy of Wood's " Plant Record," — the collector's complete outfit. 

Willis's Flora of New Jersey. 

The most useful book of reference ever published for collectors in all parts of the 
country. It contains also a Botanical Directory, with addresses of Inking American 
botanists. 

Young's Familiar Lessons in Botany. 

Combining simplicity of diction with some degree of technical and scientific knowl- 
edge, for intermediate classes. Specially adapted for the Southwest. 

Wood & Steele's Botany. 



AGRICULTURE. 

Pendleton's Scientific Agriculture. 

A text-hook for colleges and schools ; treats of the following topics : Anatomy and 
Physiology of Plants ; Agricultural Meteorology ; Soils as related to Physics ; Chemistry 
of the Atmosphere ; of Plants ; of Soils ; Fertilizers and Natural Manures ; Animal Nu- 
trition, &c. By E. M. Pendleton, M. D., Professor of Agriculture in the University of 
Georgia. 



From President A. D. White, Cornell 
University. 
" Dear Sir : I have examined your 
' Text-book of Agricultural Science,' and it 
seems to me excellent in view of the pur- 
pose it is intended to serve. Many of 
your chapters interested me especially, 
and all parts of the work seem to combine 
scientific instruction with practical infor- 
mation in proportions dictated by sound 
common 



From President Robinson, of Brown 
University. 
" It is scientific in method as well as in 
matter, comprehensive in plan, natural 
and logical in order, compact and lucid in 
its statements, and must be useful both as 
a text-book in agricultural colleges, and 
as a hand-book for intelligent planters and 
fanners." 



37 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

NATURAL SCIENCE — Continued. 

PHYSIOLOGY. 

Jarvis's Elements of Physiology. 
Jarvis's Physiology and Laws of Health. 

The only books extant which approach this subject with a proper view of the true 
object of teaching Physiology in schools, viz. , that scholars may know how to take care 
of their own health. In bold contrast with the abstract Anatomies, which children 
learn as they would Greek or Latin (and forget as soon), to disciplin.: the mind, are these 
text-books, using the science as a secondary consideration, and only so far as is neces- 
sary for the comprehension of the laws oj health. 

Steele's Physiology. 

See page 33. 



ASTRONOMY. 

Willard's School Astronomy. 

By means of clear and attractive illustrations, addressing the eye in many cases by 
analogies, careful definitions of all necessary technical terms, a careful avoidance of ver- 
biage and unimportant matter, particular attention to analysis, and a general adoption 
of the simplest methods, Mrs. Willard has made the best and most attractive elemen- 
tary Astronomy extant. 

Mclntyre's Astronomy and the Globes. 

A complete treatise for intermediate classes. Highly approved. 

Bartlett's Spherical Astronomy. 

The West Point Course, for advanced classes, with applications to the current wants 
of Navigation, Geography, and Chronology. 

Steele's Astronomy. 

See page 33. _ : . 



NATURAL HISTORY. 

Carll's Child's Book of Natural History. 

Illustrating tine animal, vegetable, and mineral kingdoms, with application to the 
arts. For beginners. Beautifully and copiously illustrated. 

Anatomical Technology. Wilder & Gage. 

As applied to the domestic cat. For the use of students of medicine. 



ZOOLOGY. 

Chambers's Elements of Zoology. 

A complete and comprehensive system of Zoology, adapted for academic instruction, 
presenting a systematic view of the animal kingdom as a portion of external nature. 

Steele's Zoology. 

See page 33. 

38 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 




LITERATURE. 



Gilman's First Steps in English Literature. 

The character and plan of this exquisite little text-book may be best understood nom 
an analysis of its contents : Introduction. Historical Period of Immature English, 
with Chart ; Definition of Terms ; Languages of Europe, with Chart ; Period of Mature 
English, with Chart ; a Chart of Bible Translations, a Bibliography or Guide to General 
Reading, and other aids to the student. 

Cleveland's Compendiums. 3 vols. 12mo. 

English Literature. American Literature. 

English Literature of the XIXth Century. 

In these volumes are gathered the cream of the literature of the English-speaking 
people for the school-room and the general reader. Their reputation is national. More 
than 125,000 copies have been sold. 

Boyd's English Classics. 6 vols. Cloth. 12mo. 

Milton's Paradise Lost. Thomson's Seasons. 

Young's Night Thoughts. Pollok's Course of Time. 

Cowper's Task, Table Talk, &c. Lord Bacon's Essays. 
This series of annotated editions of great English writers in prose and poetry is 
designed for critical reading and parsing in schools. Prof. J. R. Boyd proves himself 
an editor of high capacity, and the works themselves need no encomium. As auxiliary 
to the study of belles-lettres, &c, these works have no equal. 

Pope's Essay on Man. 16mo. Paper. 
Pope's Homer's Iliad. 32mo. Roan. 

The metrical translation of the great poet of antiquity, and the matchless "Essay on 
the Nature and State of Man," by Alexander Pope, afford superior exercise in literature 
and parsing. 



POLITICAL ECONOMY. 

Champlin's Lessons on Political Economy. 

An improvement on previous treatises, being shorter, yet containing everything 
essential, with a view of recent questions in finance, &c, wbich is not elsewhere 
found. 

39 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



^ESTHETICS. 

Huntington's Manual of the Fine Arts 

A view of the rise and progress of art in different countries, a "brief account of the 
most eminent masters of art, and an analysis of the principles of art. It is complete 
in itself, or may precede to advantage the critical work of Lord Karnes. 

Boyd's Karnes's Elements of Criticism. 

The best edition of this standard work ; without the study of which none may be 
considered proficient in the science of the perceptions. No other study can be pursued 
with so marked an effect upon the taste and refinement of the pupil. 



ELOCUTION. 

Watson's Practical Elocution. 

A scientific presentment of accepted principles of elocutionary drill, with black- 
board diagrams and full collection of examples for class drill. Cloth. 90 pages, 12mo. 

Taverner Graham's Reasonable Elocution. 

Based upon the belief that true elocution is the right interpretation of thought, 
and guiding the student to an intelligent appreciation, instead of a merely mechanical 
knowledge, of its rules. 

Zachos's Analytic Elocution. 

All departments of elocution — such as the analysis of the voice and the sentence, 
phonology, rhythm, expression, gesture, &c. — are here arranged for instruction in 
classes, illustrated by copious examples. 



SPEAKERS. 

Northend's Little Orator. 
Northend's Child's Speaker. 

Two little works of the same grade but different selections, containing simple and 
attractive pieces for children under twelve years of age. 

Northend's Young Declaimer. 
Northend's National Orator. 

Two volumes of prose, poetry, and dialogue, adapted to intermediate and grammar 
classes respectively. 

Northend's Entertaining Dialogues. 

Extracts eminently adapted to cultivate the dramatic faculties, as well as entertain. 

Oakey's Dialogues and Conversations. 

For school exercises and exhibitions, combining useful instruction. 

James's Southern Selections, for Keading and Oratory. 

Embracing exclusively Southern literature. 

Swett's Common School Speaker. 
Raymond's Patriotic Speaker. 

A superb compilation of modern eloquence and poetry, with original dramatic 
exercises. Nearly every eminent modern orator is represented. 

40 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



COMPOSITION AND RHETORIC. 

Brookfield's First Book in Composition. 

Making the cultivation of this important art feasible for the smallest child. By a 
new method, to induce and stimulate thought. 

Boyd's Composition and Rhetoric. 

This work furnishes all the aid that is needful or can be desired in the various 
departments and styles of composition, both in prose and verse. 

Day's Art of Rhetoric. 

Noted for exactness of definition, clear limitation, and philosophical development 
of subject ; the large share of attention given to invention, as a branch of rhetoric, 
and the unequalled analysis of style. 

Bardeen's Rhetoric. (In press.) 



PUNCTUATION, 



Cocker's Handbookof Punctuation. 

With instructions for capitalization, letter-writing, and proof-reading. Most works 
on this subject are so abstruse and technical that the unprofessional reader finds them 
difficult of comprehension ; but this little treatise is so simple and comprehensive that 
.persons of very ordinary intelligence can readily understand and apply its principles. 



MIND AND MORALS. 

Mahan's Intellectual Philosophy. 

The subject exhaustively considered. The author has evinced learning, candor, and 
independent thinking. 

Mahan's Science of Logic. 

A profound analysis of the laws of thought. The system possesses the merit of being 
intelligible and self-consistent. In addition to the author's carefully elaborated views, 
it embraces results attained by the ablest minds of Great Britain, Germany, and France, 
in this department. 

Boyd's Elements of Logic. 

A systematic and philosophic condensation of the subject, fortified with additions 
from Watts, Abercrombie, Whately, &c. 

Watts on the Mind. 

The " Improvement of the Mind," by Isaac Watts, is designed as a guide for theattain- 
nient of useful knowledge. As a text-book it is unparalleled ; and the discipline it 
affords cannot be too highly esteemed by the educator. 

Peabody's Moral Philosophy. 

A short course, by the Professor of Christian Morals, Harvard University, for the 
Freshman class and for high schools. 

Butler's Analogy. Hobart's Analysis. 

Edited by Prof. Charles E. West, of Brooklyn Heights Seminary. 228 pages. 16mo. 

Alden's Text-Book of Ethics. 

For young pupils. To aid in systematizing the ethical teachings of the Bible, and 
point out the coincidences between the instructions of the sacred volume and the sound 
conclusions of reason. 

41 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



GOVERNMENT. 

Howe's Young Citizen's Catechism. 

Explaining the duties of district, town, city, county, State, and United States 
officers, with rules for parliamentary and commercial business. 

Young's Lessons in Civil Government. 

A comprehensive view of Government, and abstract of the laws showing the rights, 
duties, and responsibilities of citizens. 

Mansfield's Political Manual. 

This is a complete view of the theory and practice of the General and State Govern- 
ments, designed as a text-book. The author is an esteemed and able professor of con- 
stitutional law, widely known for his sagacious utterances in the public press. 

Martin's Civil Government. 

Emanating from Massachusetts State Normal School. Historical and statistical. 
Each chapter summarized by a succinct statement of underlying principles on which 
good government is based. 

Gallaudet's International Law. 

Published in 1879, and the only work bringing the subject within the compass of a 
convenient text-book. 

Antebellum Constitutions. 

A complete collection of State and Federal Constitutions as they stood before the 
Civil War of 1861. With an essay on changes made during the reconstruction period, 
hy Wilmot L. Warren. 




First Locomotive. 

42 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

MODERN LAN GUAGES, 

A COMPLETE COURSE IN THE GERMAN. 

By James H. Worman, A.M., Professor of Modern Languages in the Adelphi Acad- 
emy, Brooklyn, L. I. 

Worman's First German Book. 
Worman's Second German Book. 
Worman's Elementary German Grammar. 
Worman's Complete German Grammar. 

These volumes are designed for intermediate and advanced classes respectively. 

Though following the same general method with " Otto " (that of " Gaspey "), our 
author differs essentially in its application. He is more practical, more systematic 
more accurate, and besides introduces a number of invaluable features which have 
never before been combined, in a German grammar. 

Among other things, it may be claimed for Professor Worman that he has been the 
first to introduce, in an American text-book for learning German, a system of analogy and 
comparison with other languages. Our best teachers are also enthusiastic about his 
methods of inculcating the art of speaking, of understanding the spoken language, of 
correct pronunciation ; the sensible and convenient original classification of nouns (in 
four declensions), and of irregular verbs, also deserves much praise. We also note the 
use of heavy type to indicate' etymological changes in the paradigms and, in the exer- 
cises, the parts which specially illustrate preceding rules. 

Worman's Elementary German Reader. 
Worman's Collegiate German Reader. 

The finest and most judicious compilation of classical and standard German literature. 
These works embrace, progressively arranged, selections from the masterpieces of 
Goethe, Schiller, Korner, Seume, Uhland, Freiligrath, Heine, Schlegel, Holty, Lenau, 
Wieland, Herder, Lessing, Kant, Fichte, Schelling, Winkehnann, Humboldt, Banke, 
Raumer, Menzel, Gervinus, &c, and contain complete Goethe's "Iphigenie," Schiller's 
"Jungfrau;" also, for instruction in modern conversational German, Benedix's 
" Eigensinn." 

There are, besides, biographical sketches of each author contributing, notes, explan- 
atory and philological (after the text), grammatical references to all leading grammars, 
as well as the editor's own, and an adequate Vocabulary. 

Worman's German Echo. 

Worman's German Copy-Books, 3 Numbers. 

On the same plan as the most approved systems for English penmanship, with 
progressive copies. 

CHAUTAUQUA SERIES. 
First and Second Books in German. 

By the natural or Pestalozzian System, for teaching the language without the help 
of the Learner's Vernacular. By James H. Worman, A. M. 

These books belong to the new Chautauqua German Language Series, and are in- 
tended for beginners learning to speak German. The peculiar features of its method 
are : — 

1. It teaches the language by direct appeal to illustrations of the objects 
referred to, and does not allow the student to guess what is said. He speaks from the 
first hour understanding! u and accurately. Therefore, 

2. Grammar is taught both analytically and synthetically throughout the 
course. The beginning is made with the auxiliaries of tense and mood, because their 
kinship with the English makes them easily intelligible ; then follow the declensions of 
nouns, articles, and other parts of speech, always systematically arranged. It is easy 
to confuse the pupil by giving him one person or one case at a time. This pernicious 
practice is discarded. Books that beget unsystematic habits of thought are worse than 
worthless. 

43 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



MODERN LANGUAGES — Continued. 



3. The ruse-s are introduced after the examples ; the purpose being to employ 
first the lower or sense faculty of the mind. 

4. Everything is taught by contrast and association, to avoid overtaxing the 
memory at the expense of the reason. 

5. The lessons convey much practical varied information, and engage the ob- 
serving as well as the thinking faculties of the learner's mind. 

In short, this brief series contains within its few pages all the essentials of German 
Grammar so presented that their mastery is easy, and the student prepared upon its 
completion to enter upon the study of the more recondite, complicated, and irregular 
principles of the language. 



From Prof. Schele de Vere, author of a 
French Grammar, Studies in English, &c. , 
&c, University of Virginia, Va. 

Prof. James H. Worman. 

My dear Sjr,— Your very liberal pub- 
lishers (Messrs. A. S. Barnes & Co.) have 
done me the honor to send me a copy of 
your excellent works, The First French and 
the Second German Book. It needed 
no introduction in the shape of compli- 
mentary notices sans nombres to call my 
attention to the eminent merits of these 
valuable publications. But I was sin- 
cerely glad that the public at large, as 
well as me, confreres litteraires dans ce 
departement de la Linguistique, have at 
length discerned the great advantages of 
your method, and enabled you and your 
publishers to bring out your works in a 
style so truly in sympathy with the in- 
trinsic value of the different volumes. 

Most unfortunately — for how I should 
delight to wield such exquisitely shaped 
and sharpened instruments to make my 
way into thick crania and dense brains ! 
— our university way of teaching does 
not admit of the admirable method pre- 
scribed in your volumes. The laws of 
the Medes are as irreversible here as the 
Decrees of Mr. Jefferson, and when I fan- 
cied I had obtained the victory, I found 
myself faced by a stern decree. All I can 
do, therefore, is to recommend your works 
most earnestly and most urgently, in the 
point of economy, to my young graduates, 
hundreds of whom leave us every harvest 
time, to scatter their seeds broadcast over 
the vast fields of the South, and to profess 
boldly their adherence to the confessions 
of their teachers. 

Wishing you heartily the best success, 
and hoping that I shall be able hereafter 
also modestly to assist you, I remain, very 
sincerely yours, Schele De Vere. 

From Head Master, Boston (Mass.) Normal 
School. 
Messrs. A. S. Barnes & Co.,— I want to 
thank you for the copies of those beautiful 



little books for beginners in German and 
French prepared by Professor Worman. 
The Professor is taking his pupils 
along the right road rapidly and delight- 
fully. 

Whatever may be said of the tedious- 
ness of learning the grammar of a new 
language, I think all will agree that the 
great labor is mastering the vocabulary. 
And it is just at this point that 1 think 
these books are of great use. The exercises 
are so developed out of pictured objects and 
actions, and are so well graduated that 
almost from the very outset they go alone. 
A beginner would have little use for 
a dictionary in reading the " First French 
Book;" and yet the words are so introduced 
and so often used, that the meaning is 
kept constantly before the mind, without 
the intervention of a translation. By this 
means the pupil soon makes them his 
permanent possession. 

A dozen volumes as well graduated as 

these would do much to give the student 

an extended vocabulary. I trust Professor 

Worman will continue his good work. 

Yours very truly, 

L. Dunton. 

From Mr. R. T. Taylor, of Beaver, Pa. 

Messrs. A. S. Barnes & Co. 

Dear Sirs, — Your kindness in sending 
books appreciated. I have examined Pro- 
fessor Worman's " First French Book " and 
I think it the best thing of the kind I have 
ever seen. There is just enough of the 
grammar combined to make the natural 
method practicable. I shall introduce 
the work into my school this fall. We have 
been using Professor Worman's German 
books and are very much pleased with 
them. The "Echo," in particular, de~ 
lights pupils. They make more advance- 
ment in one year by this method than in 
two by the old manner of teaching. 

Wishing you success in your business. 
I am 

Yours very truly, 

R. T. Taylop- 



44 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



FRENCH. 



Worman's First Book in French. 

The first book in the companion series to the successful German Series by the same 
author, and intended for those wishing to speak French. The peculiar features of Pro- 
fessor Worman's new method are : — 



10. 



The French language is taught without the help of English. 

It appeals to pictorial illustrations for the names of objects. 

The learner speaks from the tirst hour under standingly. 

Grammar is taught to prevent missteps in composition. 

The laws of the language are taught analytically to make them the learner's own 

inferences (— deductions). 
Rapidity of progress by dependence upon association and contrasts. 
Strictly graded lessons and conversations on familiar, interesting, and instructive 

topics, providing the words and idioms of every-day life. . 
Paradigms to give a systematic treatment to variable inflections. 
Heavy type for inflections, to make the eye a help to the mind. 
Hair line type for the silent letters, and links for words to be connected, in order 

to teach an accurate pronunciation. 

Worman's French Echo. 

This is not a mass of meaningless and parrot-like phrases thrown together for 
a tourist's use, to bewilder him' when in the presence of a Frenchman. 

The " Echo de Paris " is a strictly progressive conversational book, beginning with sim- 
ple phrases and leading by frequent repetition to a mastery of the idioms and of the 
every-day language used in business, on travel, at a hotel, in the chit-chat of 
society. 

It presupposes an elementary knowledge of the language, such as may be acquired 
from the First French Book by Professor Worrnan, and furnishes a running French 
text, allowing the learner of course to find the meaning of the words (in the appended 
Vocabulary), and forcing him, by the absence of English in the text, to think in 
French. 



Chek Monsieur Worman, — Vousme 
demandez raon opinion sur votre " Echo de 
Paris" et quel usage j'en fais. Je ne 
saurais mieux vous repondre qu'en repro- 
duisant une lettre que j'ecrivais derniere- 
ment a un collegue qui etait, me disait-il, 
"bien fatigue de ces insipides livres de 
dialogues. " 

" Vous ne connaissez done pas," lui 
disais-je, " TEcho de Paris,' edite par le 
Professor Worman? C'est un veritable 
tresor, merveilleusemetit adapte au devel- 
oppement de la conversation familiere et 
pratique, telle qu'on la veut aujourd'hui. 
Cet excellent livre met successivement en 
scene, d'une maniere vive et interessante, 



toutes les circonstances possibles de la vie 
ordinaire. Voyez l'immense avantage 
il vous transporte en France ; du premier 
mot, je m'imagine, et mes eleves avec moi, 
que nous sonimes a Paris, dans la rue, sur 
une place, dans une gare, dans un salon, 
dans une chambre, voire meme a la cui- 
sine ; je parle comme avec des Francais ; 
les eleves ne songent pas a traduire de 
Panglais pour me repondre ; ils pensent 
en francais ; ils sont Frangais pour le 
moment par les yeux, par l'oreille, par la 
pensee. Quel autre livre pourrait produire 
cette illusion? ..." 

Votre tout devoue, 

A. DE ROUGEMONT. 



Illustrated Language Primers. 

French and English. German and English. 

Spanish and English. 

The names of common objects properly illustrated and arranged in easy lessons. 

Pujol's Complete French Class-Book. 

Offers in one volume, methodically arranged, a complete French course — usually 
embraced in series of from five to twelve books, including the bulky and expensive 
lexicon. Here are grammar, conversation, and choice literature, selected from the 
best French authors. Each branch is thoroughly handled ; and the student, having 
diligently completed the course as prescribed, may consider himself, without further 
application, au fait in the most polite and elegant language of modern times. 

45 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



. MODERN LANGUAGES — Continued-. 

Pujol's French Grammar, Exercises, Reader. 3 vols. 

These volumes contain Part I., Parts II. and III., and Part IV. of the Complete Class- 
Book respectively, for the convenience of scholars and teachers. The Lexicon is bound 
with each part. 

Maurice-Poitevin's Grammaire Francaise. 

American schools are at last supplied with an American edition of this famous text- 
book. Many of our best institutions have for years been procuring it from abroad 
rather than forego the advantages it offers. The policy of putting students who have 
acquired some proficiency from the ordinary text-books, into a Grammar written in the 
vernacular, cannot be too highly commended. It affords an opportunity for finish and 
review at once, while embodying abundant practice of its own rules. 



ANCIENT LANGUAGES, 




LATIN. 

Searing's Virgil's ^neid. 

1. It contains only the first six books of the ^Eneid. 2. A very carefully constructed 
Dictionary. 3. Sufficiently copious notes. 4. Grammatical references to four leading 
Grammars. 5. Numerous illustrations of the highest order. 6. A superb map of the 
Mediterranean and adjacent countries. 7. Dr. S. H. Taylor's " Questions on the JSneid. " 
8. A Metrical Index, and an essay on the Poetical Style. 9. A photographic facsimile 
of an early Latin MS. 10. The text is according to Jahn, but paragraphed according 
to Ladewig. 11. Superior mechanical execution. 



"My attention was called to Searing's 
Virgil by the fact of its containing a vo- 
cabulary which would obviate the neces- 
sity of procuring a lexicon. But use in 
the class-room has impressed me most 
favorably with the accuracy and just pro- 
portion of its notes, and the general ex- 
cellence of its grammatical suggestions. 
The general character of the book, in its 



paper, its typography, and its engravings, 
is highly commendable, and the facsimile 
manuscript is a valuable feature. I take 
great pleasure in commending the book to 
all who do not wish a complete edition of 
Virgil. It suits our short school courses 
admirably." — Henry L. Bolt wood, Mas- 
ter Princeton High School, III. 



46 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 




GREEK. 

Scarborough's First Lessons in Greek. 

A new two-term text-book, with copious notes and references to the Grammars of 
Goodwin and Hadley, and an adequate Vocabulary. Designed as an Elementary Drill- 
book on the inflections and syntax of the Greek language. 

I. These Lessons embrace all the essential points of the Greek etymology and syn- 
tax, and are sufficient to introduce the learner to Goodwin's Greek Reader, Xenophon's 
Anabasis, or similar Greek. 

II. The notes and references are full enough in every particular to give the 
student a thorough knowledge of the rudimentary forms, inflections, and principles of 
the Greek language. 

III. The verb is introduced early, so that the inflections of nouns and verbs 
are given side by side, and the pupil is at once made acquainted with complete 
sentences. 

IV. As the student advances, the principles of Greek syntax are gradually developed 
so that he is led step by step from the simple to the more complex. 

V. The book is divided into two parts. The first consists of seventy-eight lessons, 
with Greek and English lessons alternating. The second, of selections from the 
Anabasis (parts of the 1st and 6th chapters, Bk. I.) and the Memorabilia (the Choice of 
Hercules, Bk. II., chapter 1). 

VI. The book is sufficient for all piirposes in rudimentary instruction. i 



From The Religious Herald, Hartford, Ct. 
" We are highly pleased with this ele- 
mentary work. The eighty-five lessons of 
part first may well be taken in fifteen to 
twenty weeks, and part second may be 
pursued to advantage, or the scholar may 
go directly from the first part to the Ana- 
basis. The arrangement of lessons is 
good, which the teacher will employ at 
his discretion so as to secure the most 
efficient work of his classes." 

" I have examined Professor Scarbo- 
rough's ' First Lessons in Greek ' with 
some care, and am much interested in 



the book. It is clear and accurate, de- 
velopes the subject naturally and easily 
and is handsomely printed. The methods 
of a practical teacher are everywhere 
seen." Wm. G. Frost, 

Professor of Greek, Oberlin College, Ohio. 

"I have examined. Professor Scarbo- 
rough's ' First Lessons in Greek ' with 
much care. I am exceedingly well pleased 
with the work and think it in every way 
well adapted to the uses for which it is 
intended. " 

"Wm. H. Tibball, 
Principal of Poland (0.), Seminary. 



47 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 




Thermopylae. 
[Specimen Illustration from Barnes's Brief History of Ancient Peoples.] 



48 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



SCHOOL MUSIC. 

The National School Singer. 

Bright, new music for the day school, embracing Song Lessons, Exercise Songs, Songs 
of Study, Order, Promptness, and Obedience, of Industry and Nature, Patriotic and 
Temperance Songs, Opening and Closing Songs ; in fact, everything needed in the 
school-room. By an eminent musician and composer. 

Jepson's Music Readers. 3 vols. 

These are not books from which children simply learn songs, parrot-like, but teach 
the subject progressively, the scholar learning to read music by methods similar to 
those employed in teaching him to read printed language. Any teacher, however igno- 
rant of music, provided he can, upon trial, simply sound the scale, may teach it without 
assistance, and will end by being a good singer himself. The " Elementary Music 
Reader," or first volume, fuily develops the system. The two companion volumes carry 
the same method into the higher grades, but their use is not essential. 

The First Reader is also published in three parts, at thirty cents each, for those who 
prefer them in that form. 

Nash and Bristow's Cantara. 

The first volume is a complete musical text-book for schools of every grade. No. 2 is 
a choice selection of solos and part songs. The authors are Directors of Music 
in the public schools of New York City, in which these books are the standard of 
instruction. 

The Polytechnic. 

Collection of Part Songs for High and Normal Schools and Clubs. This work con- 
tains a quantity of exceedingly valuable material, heretofore accessible only in sheet 
form or scattered in numerous and costly works. The collection of " College Songs " 
is a very attractive feature. 

Curtis's Little Singer, — School Vocalist. 

Kingsley's School-Room Choir, — Young Ladies' 

Harp. 
Hager's Echo (A Cantata). 



SCHOOL DEVOTIONAL EXERCISE. 

Brooks's School Manual of Devotion. 

This volume contains daily devotional exercises, consisting of a hymn, selections of 
Scripture for alternate reading by teacher and pupils, and a prayer. Its value for open- 
ing and closing school is apparent. 

Brooks's School Harmonist. 

Contains appropriate tunes for each hymn in the " Manual of Devotion " described 
above. 

Bartley's Songs for the School. 

A selection of appropriate hymns of an unsectarian character, carefully classified 
and set to popular and "singable " tunes, for opening and closing exercises. The Secu- 
lar Department is full of bright and well-selected music. 

49 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 
TEACHERS' AIDS AND SCHOOL REQUISITES. 

CHARTS AND MAPS. 

Baade's Reading Case. 

This remarkable piece of school-room furniture is a receptacle containing a number 
of primary cards. By an arrangement of slides on the front, one sentence at a time is 
shown to the class. Twenty-eight thousand transpositions may be made, affording a 
variety of progressive exercises which no other piece of apparatus offers. One of its 
best features is, that it is so exceedingly simple as not to get out of order, while it may 
be operated with one finger. 

Clark's Grammatical Chart. 

Exhibits the whole science of language in one comprehensive diagram. 

Davies's Mathematical Chart. 

Elementary mathematics clearly taught to a full class at a glance. 

De Rupert's Philological and Historical Chart. 

This very comprehensive chart shows the birth, development, and progress of the 
literatures of the world ; their importance, their influence on each other, and the cen- 
tury in which such influence was experienced ; with a list for each country of standard 
authors and their best works. Illustrating also the division of languages into classes, 
families, and groups. Giving date of settlement, discovery, or conquest of all countries, 
with their government, religion, area, population, and the percentage of enrolment for 
1872, in the primary schools of Europe and America. 

Eastman's Chirographic Chart. Family Record. 
Gimns's Number Chart. 

Teaches addition, subtraction, multiplication, and division. Size, 23x31 inches. ■ 

Marcy's Eureka Tablet. 

A new system for the alphabet, by which it may be taught without fail in nine lessons. 

McKenzie's Elocutionary Chart. 
Monteith's Pictorial Chart of Geography. 

A crayon picture illustrating all the divisions of the earth's surface commonly 
taught in geography. 



in all good geographies. I think the 
chart would be a great help in any pri- 
mary department." 



Wm. L. Dickinson, Superintendent of 

Schools, Jersey City, says. 
" It is an admirable amplification of the 
system of pictorial illustration adopted 

Monteith's Reference Maps. School and Grand Series. 

Names all laid down in small type so that to the pupil at a short distance they are 
outline maps, while they serve as their own key to the teacher. 

Page's Normal Chart. 

The whole science of elementary sounds tabulated. 

Scofield's School Tablets. 

On five cards, exhibiting ten surfaces. These tablets teach orthography, reading, 
object-lessons, color, form, &c. 

Watson's Phonetic Tablets. 

Four cards and eight surfaces ; teaching pronunciation and elocution phonetically. 
For class exercises. 

Whitcomb's Historical Chart. 

A student's topical historical chart, from the creation to the present time, including 
results of the latest chronological research. Arranged with spaces for summary, that 
pupils may prepare and review their own chart in connection with any text-book. 

Willard's Chronographers. 

Historical. Four numbers : Ancient chronographer, English chronographer, Ameri- 
can chronographer, temple of time (general). Dates and events represented to the eye. 

50 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 

". 

APPARATUS. 

Bock's Physiological Apparatus. 

A collection of twenty-seven anatomical models. 

Harrington's Fractional Blocks. 
Harrington's Geometrical Blocks. 

These patent blocks are hinged, so that each form can be dissected. 

Kendall's Lunar Telluric Globe. 

Moon, globe, and tellurian combined. 

Steele's Chemical Apparatus. 
Steele's Geological Cabinet. 
Steele's Philosophical Apparatus. 
Wood's Botanical Apparatus. 



RECORDS. 

Cole's Self-Reporting Class Book. 

Foi saving the teacher's labor in averaging. At each opening are a full set of tables 
showing any scholar's standing at a glance, and entirely obviating the necessity of 
computation. 

Tracy's School Record. {SSn] 

For keeping a simple but exact record of attendance, deportment, and scholarship. 
The larger edition contains also a calendar, an extensive list of topics for compositions 
and colloquies, themes for short lectures, suggestions to young teachers, &c. 

Benet's Individual Records. 
Brooks's Teacher's Register. 

Presents at one view a record of attendance, recitations, and deportment for the 
whole term. 

Carter's Record and Roll-Book. 

This is the most complete and convenient record offered to the public. Besides the 
usual spaces for general scholarship, deportment, attendance, &c, for each name and 
day, there is a space in red lines enclosing six minor spaces in blue for recording 
recitations. 

National School Diary. 

A little book of blank forms for weekly report of the standing of each scholar, from 
teacher to parent. A great convenience. 



REWARDS. 

National School Currency. 

A little box containing certificates in the form of money. The most entertaining and 
stimulating system of school rewards. The scholar is paid for his merits and fined for 
his short-comings. Of course the most faithful are the most successful in business. 
In this way the use and value of money and the method of keeping accounts are also 
taught. One box of currency will supply a school of fifty pupils. 

51 



THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



PENMANSHIP, PENS, &c. 

Beers's System 
Per dozen . 



of Progressive Penmanship. 



This " round hand " system of Penmanship, in twelve numbers, commends itself by 
its simplicity and thoroughness. The first four numbers are primary books. Nos. 5 to 
7, advanced books for boys. Nos. 8 to 10, advanced books for girls. Nos. 11 and 12, 
ornamental penmanship. These books are printed from steel plates (engraved by 
McLees), and are unexcelled in mechanical execution. Large quantities are annually 
sold. 

Beers's Slated Copy Slips. Per set 

All beginners should practise, for a few weeks, slate exercises, familiarizing them 
with the form of the letters, the motions of the hand and arm, &o, &c. These copy 
slips, 32 in number, supply all the copies found in a complete series of writing-" 
at a trifling cost. 



Payson, Dunton, 
Per dozen . . 



& Scribner's Copy-Books. 



The National System of Penmanship, in three distinct series : (1) Common 
School Series, comprising the first six numbers ; (2) Business Series, Nos. 8, 11, and 
12 ; (3) Ladies' Series, Nos. 7, 9, and 10. 

Fulton & Eastman's Chirographic Charts . . 

To embellish the school-room walls, and furnish class exercise in the elements of 
Penmanship. 

Payson's Copy-Book Cover. Per hundred . . 

Protects every page except the one in use, and furnishes "lines " with proper slope 
for the penman, under. Patented. 

National Steel Pens. Card with all kinds . . . 

Pronounced by competent judges the perfection of American-made pens, and supe- 
rior to any foreign article. 



SCHOOL SERIES. 
School Pen, per gross .... 

Academic Pen do 

Fine Pointed Pen , per gross . . 

POPULAR SERIES. 
Capitol Pen, per gross . . . . 



do. do. per box of 2 doz. . 
Bullion Pen (imit. gold) per gross 
Ladies' Pen do. . 



$0.60 
.63 

.70 



$1.00 
.25 
.75 
.63 



Index Pen, per gross .... 
BUSINESS SERIES. 



.75 



Albata Pen, per i_ 
Bank Pen, do. 
Empire Pen do. . . 

Commercial Pen, per gross 

Express Pen, do. 

Falcon Pen, do. 

Elastic Pen, do. 



$0.40 
.70 
.70 
.60 
.75 
.70 
.75 



Stimpson's Scientific Steel Pen. Per gross . . $1.50 

One forward and two backward arches, ensuring great strength, well-balanced elas- 
ticity, evenness of point, and smoothness of execution,. One gross in twelve contains a 
Scientific Gold Pen. 

Stimpson's Ink-Retaining Holder. Per dozen . $1.50 

A simple apparatus, which does not get out of order, withholds at a single dip as 
much ink as the pen would otherwise realize from a dozen trips to the inkstand, which 
it supplies with moderate and easy flow. 

Stimpson's Gold Pen, $3.00 ; with Ink Retainer . $4.50 
Stimpson's Penman's Card 25 

One dozen Steel Pens (assorted points) and Patent Ink-retaining Pen-holder. 



_. 52 



THE NATIONAL SERIES OF STANDARD MISCELLANY. 

LIBRARY AND MISCELLANEOUS 
PUBLICATIONS. 



TEACHERS' WORKING LIBRARY. 
Object Lessons. Welch. 

This is a complete exposition of the popular modern system of "object-teaching," 
for teachers of primary classes. 

Theory and Practice of Teaching. Page. 

This volume has, without doubt, been read by two hundred thousand teachers, and 
its popularity remains undiminished, large editions being exhausted yearly. It was 
the pioneer, as it is now the patriarch, of professional works for teachers. 

The Graded School. Wells. 

The proper way to organize graded schools is here illustrated. The author has availed 
himself of the best elements of the several systems prevalent in Boston, New York, 
Philadelphia, Cincinnati, St. Louis, and other cities. 

The Normal. Holbrook. 

Carries a working school on its visit to teachers, showing the most approved methods 
of teaching all the common branches, including the technicalities, explanations, demon- 
strations, and definitions introductory and peculiar to each branch. 

School Management. Holbrook. 

Treating of the teacher's qualifications ; how to overcome difficulties in self and 
others ; organization ; discipline ; methods of inciting diligence and order ; strategy 
in management ; object-teaching. 

The Teachers' Institute. Fowle. 

This is a volume of suggestions inspired by the author's experience at institutes, in 
the instruction of young teachers. A thousand points of interest to this class are most 
satisfactorily dealt with. 

Schools and Schoolmasters. Dickens. 

Appropriate selections from the writings of the great novelist. 

The Metric System. Davies. 

Considered with reference to its general introduction, and embracing the views of 
John Quincy Adams and Sir John Herschel. 

The Student ; The Educator. Phelps. 2 vols. 
The Discipline of Life. Phelps. 

The authoress of these works is one of the most distinguished writers on education, 
and they cannot fail to prove a valuable addition to the School and Teachers' Libraries, 
being in a high degree both interesting and instructive. 

Law of Public Schools. Burke. 

By Finley Burke, Counsellor-at-Law. A new volume in " Barnes's Teachers' Library 
Series." 12mo, cloth. 



"Mr. Burke has given us the latest 
expositions of the law on this highly im- 
portant subject. I shall cordially com- 
mend his treatise." — Theodore Dwight, 
LL.D. 

From the Hon. Joseph M. Beck, Judge of 
Supreme Court, Iowa. 

" I have examined with considerable 
"^are the manuscript of ' A Treatise on the 



Law of Public Schools.' by Finley Burke, 
Esq., of Council Bluffs. In my opinion, 
the work will be of great value to school 
teachers and school officers, and to law- 
yers. The subjects treated of are thought- 
fully considered and thoroughly examined, 
and correctly and systematically arranged. 
The style is perspicuous. The legal doc- 
trines of the work, so far as I have been 



53 



THE NATIONAL SERIES OF STANDARD MISCELLANY. 



MISCELLANEOUS PUBLICATIONS — Continued. 



able to consider them, are sound. I have 
examined quite a number of the authori- 
ties cited ; they sustain the rules an- 
nounced in the text. Mr. Burke is an able 
and industrious member of the bar of the 
Supreme Court of this State, and has a 
high standing in the profession of the 
law." 

" I fully concur in the opinion of Judge 
Beck, above expressed." — John F. Dil- 
lon. New York, May, 1880. 

Sioux City, Iowa, May, 1880. 
I have examined the manuscript of 
Finley Burke, Esq. , and iihd a full citation 
of all the cases and decisions pertaining to 
the school law, occurring in the courts of 
the United States. This volume contains 

Teachers' Handbook. Phelps. 

By William F. Phelps, Principal of Minnesota State Normal School. Embracing the 
objects, history, organization, and management of teachers' institutes, followed by 
methods of teaching, in detail, for all the fundamental branches. Every young teacher, 
every practical teacher, every experienced teacher even, needs this book. 

This is the key-note of the present excel- 



valuable and important information con- 
cerning school law, which has never before 
been accessible to either teacher or school 
officer. A. Armstrong, 

Supt. Schools, Sioux City, Iowa. 

Des Moines, May 15, 1880.' 
The examination of " A Treatise on the 
Law of Public Schools," prepared by Fin- 
ley Burke, Esq. , of Council Bluffs, has 
given me much pleasure. So far as I 
know, there is no work of similar charac- 
ter now in existence. I think such a work 
will be exceedingly useful to lawyers, 
school officers, and teachers, and I hope 
that it may find its way into their hands. 
G. W. von Coelln, 

Supt. Public Inst, for Iowa. 



lent volume. In view of the supreme 
importance of the teacher's calling, Mr. 
Phelps has presented an elaborate system 
of instruction in the elements of learning, 
with a complete detail of methods and 
processes, illustrated with an abundance 
of practical examples and enforced by 
judicious councils." 



From the New York Tribune. 

"The discipline of the school should 

Prepare the child for the discipline of life, 
he country schoolmaster, accordingly, 
holds a position of vital interest to the 
destiny of the republic, and should neg- 
lect no means for the wise and efficient 
discharge of his significant functions. 

Topical Course of Study. Stone. 

This volume is a compilation from the courses of study of our most successful public 
schools, and the best thought of leading educators. The pupil is enabled to make full 
use of any and all text-books bearing on the given topics, and is incited to use all other 
information within his reach. 

American Education. Mansfield. 

A treatise on the principles and elements of education, as practised in this country, 
with ideas towards distinctive republican and Christian education. 

American Institutions. De Tocqueville. 

A valuable index to the genius of our Government. 

Universal Education. Mayhew. 

The subject is approached with the clear, keen perception of one who has observed 
its necessity, and realized its feasibility and expediency alike. The redeeming and 
elevating power of improved common schools constitutes the inspiration of the volume. 

Oral Training Lessons. Barnard. 

The object of this very useful work is to furnish material for instructors to impart 
orally to their classes, in branches not usually taught in common schools, embracing all 
departments of natural science and much general knowledge. 

Lectures on Natural History. Chadbourne. 

Affording many themes for oral instruction in this interesting science, especially in 
schools where it is not pursued as a class exercise. 



54 



THE NATIONAL SERIES OF STANDARD MISCELLANY. 

MISCELLANEOUS PUBLICATIONS — Continued. 

Outlines of Mathematical Science. Davies. 

A manual suggesting the best methods of presenting mathematical instruction on the 
part of the teacher, with that comprehensive view of the whole which is necessary to 
the intelligent treatment of a part, in science. 

Nature and Utility of Mathematics. Davies. 

An elaborate and lucid exposition of the principles which lie at the foundation of 
pure mathematics, with a highly ingenious application of their results to the develop- 
ment of the essential idea of the different branches of the science. 

Mathematical Dictionary. Davies arfd Peck. 

This cyclopaedia of mathematical science defines, with completeness, precision, and 
accuracy, every technical term ; thus constituting a popular treatise on each branch, 
and a general view of the whole subject. 

How Not to Teach. Giffin. 

A collection of one hundred things the teacher should not do, with the reasons why. 
Also, an appendix, containing apt quotations for use in schools. 

How to Teach. .Giffin. (In press.) 
The Popular Educator. Barnes. 

In seven volumes, containing interesting and profitable educational miscellany. 

Liberal Education of Women. Orton. 

Treats of " the demand and the method ; " being a compilation of the best and most 
advanced thought on this subject, by the leading writers and educators in England and 
America. Edited by a professor in Vassar College. 

Education Abroad. Northrop. 

A thorough discussion of the advantages and disadvantages of sending American 
children to Europe to be educated ; also, papers on legal prevention of illiteracy, study, 
and health, labor as an educator, and other kindred subjects. 

The Teacher and the Parent. Northend. 

A treatise upon common-school education, designed to lead teachers to view their 
calling in its true light, and to stimulate them to fidelity. 

The Teachers' Assistant. Northend. 

A natural continuation of the author's previous work, more directly calculated for 
daily use in the administration of school discipline and instruction. 

School Government. Jewell. 

Full of advanced ideas on the subject which its title indicates. The criticisms upon 
current theories of punishment and schemes of administration have excited general 
attention and comment. 

Grammatical Diagrams. Jewell. 

The diagram system of teaching grammar explained, defended, and improved. The 
curious in literature, the searcher for truth, those interested in new inventions, as well 
as the disciples of Professor Clark, who would see their favorite theory fairly treated, 
all want this book. There are many who would like to be made familiar with this 
system before risking its use in a class. The opportunity is here afforded. 

The Complete Examiner. Stone. 

Consists of a series of questions on every English branch of school and academic 
instruction, with reference to a given page or article of leading text-books where the 
answer may be found in full. Prepared to aid teachers in securing certificates, pupils 
in preparing for promotion, and teachers in selecting review questions. 

55 



THE NATIONAL SERIES OF STANDARD MISCELLANY, 

MISCELLANEOUS PUBLICATIONS — Continued. 

School Amusements. Root. 

To assist teachers in making the school interesting, with hints upon the manage- 
ment of the school-room. Rules for military and gymnastic exercises are included. 
Illustrated by diagrams. 

Institute Lectures. Bates. 

These lectures, originally delivered before institutes, are based upon various topics in 
the departments of mental and moral culture. The volume is calculated to prepare 
the will, awaken the inquiry, and stimulate the thought of the zealous teacher. 

Method of Teachers' Institutes. Bates. 

Sets forth the best method of conducting institutes, with a detailed ^account of the 
object, organization, plan of instruction, and true theory of education on which such 
instruction should be based. 

History and Progress of Education. 

The systems of education prevailing in all nations and ages, the gradual advance to 
the present time, and the bearing of the past upon the present, in this regard, are 
worthy of the careful investigation of all concerned in education. 

Higher Education. Atlas Series. 

A collection of valuable essays. Contents. International Communication by Lan- 
guage, by Philip Gilbert Hamerton ; Reform in Higher Education ; Upper Schools, by 
President James McCosh ; Study of Greek and Latin Classics, by Prof. Charles 
Elliott ; The University System in Italy, by Prof. Angelo de Gubernatis, of the 
University of Florence ; Universal Education, by Ray Palmer ; Industrial Art Educa- 
tion, by Eaton S. Drone. 



LIBRARY OF LITERATURE. 

Milton's Paradise Lost. (Boyd's Illustrated Edition.) 
Young's Night Thoughts. do. 

Cowper's Task, Table Talk, &c. do. 
Thomson's Seasons. do. 

Pollok's Course of Time. do. 

These works, models of the best and purest literature, are beautifully illustrated, and 
notes explain all doubtful meanings. 

Lord Bacon's Essays. (Boyd's Edition.) 

Another grand English classic, affording the highest example of purity in language 
and style. 

The Iliad of Homer. (Translated by Pope.) 

Those who are unable to read this greatest of ancient writers in the original should 
not fail to avail themselves of this standard metrical version. 

Pope's Essay on Man. 

This is a model of pure classical English, which should be read, also, by every teacher 
and scholar for the sound thought it contains. 

Improvement of the Mind. Isaac Watts. 

No mental philosophy was ever written which is so comprehensive and practically 
useful to the unlearned as well as learned reader as this well-known book of Watts. 

Milton's Political "Works. Cleveland. 

This is the very best edition of the great poet. It includes a life of the author, 
notes, dissertations on each poem, a faultless text, and is the only edition of Milton 
with a complete verbal index. 

5e 



THE NATIONAL SERIES OF STANDARD MISCELLANY, 

MISCELLANEOUS PUBLICATIONS — Continued. 

Compendium of English Literature. Cleveland. 
English Literature of XlXth Century. Cleveland. 
Compendium of American Literature. Cleveland. 

Nearly one hundred and fifty thousand volumes of Professor Cleveland's inimitable 
compendiums have been sold. Taken together they present a complete view of litera- 
ture. To the man who can afford but a few books these will supply the place of an 
extensive library. From commendations of the very highest authorities the following 
extracts will give some idea of the enthusiasm with which the works are regarded by 
scholars : — 

" With the Bible and your volumes one might leave libraries without very painful 
regret." " The work cannot be. found from which in the same limits so much interesting 
and valuable information may be obtained." " Good taste, fine scholarship, familiar 
acquaintance with literature, unwearied industry, tact acquired by practice, an interest 
in the culture of the young, and regard for truth, purity, philanthropy, and religion 
are united in Mr. Cleveland." " A judgment clear and impartial, a taste at once deli- 
cate and severe." "The biographies are just and discriminating." "An admirable 
bird's-eye view." "Acquaints the reader with the characteristic method, tone, and 
quality of each writer." " Succinct, carefully written, and wonderfully comprehensive 
in detail," &c, &e. 




■ Mi i in- inn I't.'jjfc 
Old New York Plate. 



[From Mrs. Martha J. Lamb's " History of the City of New York."] 
57 




Illustration from Barnes's "History of Ancient Peopws." 

58 



THE NATIONAL SERIES OF STANDARD MISCELLANY, 

MISCELLANEOUS PUBLICATIONS - Continued. 

LIBRARY OF HISTORY. 
Ancient and Mediaeval Republics. Mann. 

A review of their institutions, and of the causes of their decline and fall. By 
Henry Mann. "8vo. 584 pages, cloth. 

Outlines of General History. Gilman. 

The number of facts which the author has compressed into these outline sketches is 
really surprising ; the chapters on the Middle Ages and feudalism afford striking ex- 
amples of his power of succinct but comprehensive statement. In his choice of 
representative periods and events in the histories of nations he shows very sound judg- 
ment, and his characterization of conspicuous historical figures is accurate and 
impartial. 

Great Events of History. Collier. 

This celebrated work, edited for American readers by Prof. 0. R. Willis, gives, in a 
series of pictures, a pleasantly readable and easily remembered view of the Christian 
era. Each chapter is headed by its central point of interest to afford association for the 
mind. Delineations of life and manners at different periods are interwoven. A geo- 
graphical appendix of great value is added. 

History of England. Lancaster. 

An arrangement of the essential facts of English history in the briefest manner 
consistent with clearness. With a fine map. 

A Critical History of the Civil War. Mahan. 

ByAsaMahan, LL.D., author of "Intellectual Philosophy," "Elements of Logic," 
&c. * First president of Oberlin College, Ohio. With au introductory letter by Lieut- 
Gen. M. W. Smith of the British army. 8vo. 450 pages. Cloth. 

The plan of this work is to present, not the causes and details of facts which led to 
the war, but the conduct and management of the war on the part of those concerned. 
It is a matter of present and future importance to Americans to know not only how the 
war was conducted, but also how it might have been more successfully carried on. 
The author has made the science of war a subject of careful and protracted study, and 
his views are pronounced and scientific. He takes strong ground, writes with vigor, 
and the interest of the reader is fully sustained from the beginning to the close of the 
book. His conclusions have already passed into history, and this work will be regarded 
as one of the most important contributions to the literature of the subject. 

Europe under Napoleon First. Alison. 

A history of Europe from 17S9 to 1815. By Archibald Alison. Abridged by Edward 
S. Gould. ' 1 vol. 8vo, with appendix, questions, and maps. 550 pages. 

"One of the best abridgments lever 
saw. The material facts are all retained, 
and Mr. Gould has displayed great indus- 
try and skill in preserving the substance 
of so great a history." — Chancellor 
James Kent. 

History of Rome. Ricord. 

An entertaining narrative for the young. Illustrated. Embracing successively, The 
Kings, The Republic, The Empire. 

-History of the Ancient Hebrews. Mills. 

The record of "God's people" from the call of Abraham to the destruction of Jeru- 
salem ; gathered from sources sacred and profane. 

The Mexican War. Mansfield. 

A history of its origin, and a detailed account of its victories ; with official despatches, 
the treaty of peace, and valuable tables. Illustrated. 

59 



" It seems to me an excellent abridg- 
ment. . . . Written in clear and chaste 
style, presenting the narrative in exact 
form for the general reader. . . . "—Judge 
Joseph Story. 



THE NATIONAL SERIES OF STANDARD MISCELLANY 



MISCELLANEOUS PUBLICATIONS — Continued. 

Early History of Michigan. Sheldon. 

A work of value and deep interest to the people of the West. Compiled undnr the 
supervision of Hon. Lewis Cass. Portraits. 

History of Texas. Baker. 

A pithy and interesting resume. Copiously illustrated. The State constitution and 
extracts from the speeches and writings of eminent Texans are appended. 

Magazine of American History. 

8 volumes. Illustrated. A collection of valuable data relating to American 
History. 

Points of History. 

For schools and colleges. By John Lord, LL.D. , author of "Old Roman World," 
" Modern History," &c. 

Barnes's Popular History of the United States. 1 vol. 

This superbly illustrated work is by the author of " Barnes's Brief Histories " (for 
schools). The leading idea is to make American history popular for the masses, and 
especially with the young. The style is therefore life-like and vivid, carrying the 
reader along by the sweep of the story as in a novel, so that when he. begins an account 
of an important event he cannot very well lay down the book until he finishes. It is 
complete from the earliest times to date. 

" Barnes's Popular History of the United States " was undertaken at the close of the 
first hundred years of American Independence. The author proposed to give to the 
whole people of the United States and the world a thoroughly impartial history of 
America, from the rnound-builders to the present time. As such it was necessary to 
steer free from whatever in recent history would arouse sectional animosity or party 
bitterness. He determined to meet all questions of burning moment in the judicial 
rather than controversial spirit, and while giving to every event its due importance, he 
would seek to avoid controversy by the gentle word "that turneth away wrath." The 
work is now finished down to President Arthur's administration. In it the truth of 
American history is impartially given in true historic form, without fear or favor. It is 
a work that all sections of the country can read and enjoy. Although the author is a 
Northern man and soldier, his work is popular and widely used as a text-book East, 
West, North, and South. An Alabama teacher lately wrote as follows : " We are lising 
your history and like it, though it does n't favor us rebels." And so it is liked throughout 
the country, because it does n't favor any side at the expense of truth and justice. 
Instead of being spread out in many volumes, more or less didactic, statistical, or dry, 
the book is complete in one royal 8vo volume of 850 pages, with 14 full-page steel 
engravings and 320 text illustrations on wood, engraved by eminent artists. It is fully 
up to the times and includes an account of President Garfield's brief administration 
and tragic death. 

Mrs. Martha J. Lamb's History of New York City. 
2 vols., cloth. 

This is a complete survey of the history of New York from early settlement to the 
present time. It opens with a brief outline of the condition of the Old World prior to 
the settlement of the New, and proceeds to give a careful analysis of the two great 
Dutch Commercial Corporations to which New York owes its origin. It sketches the 
rise and growth of the little colony on Manhattan Island ; describes the Indian wars 
with which it was afflicted ; gives color and life to its Dutch rulers ; paints its subju- 
gation by the English, its after vicissitudes, the Revolution of 1689 ; in short, it leads 
the reader through one continuous chain of events down to the American Revolution. 
Then, gathering up the threads, the author gives an artistic and comprehensive account 
of the progress of the city, in extent, education, culture, literature, art, and political 
and commercial importance during the last century. Prominent persons are introduced 
in all the different periods, with choice bits of family history, and glimpses of social 
life. The work contains maps of the city in the different decades, and several rare 

60 



THE NATIONAL SERIES OF STANDARD MISCELLANY, 

MISCELLANEOUS PUBLICATIONS — Continued. 

portraits from original paintings, which have never before been engraved. The illus- 
trations, about 320 in number, are all of an interesting and highly artistic character. 



''Widely welcomed both for its abun- 
dant stores of information and the attrac- 
tions of the narrative." — New York 
Tribune. 



" There is warmth and color and life in 
every passage. " — New York Siln. 

" The work has been done faithfully 
and picturesquely." — The Nation. 



Carrington's Battles of the Revolution. 

A careful description and analysis of every engagement of the War for Independence, 
with topographical charts prepared from personal surveys by the author, a veteran 
officer of the United States army, and Professor of Military Science in Wabash College. 

Baker's Texas Scrap-Book. 

Comprising the history, biography, literature, and miscellany of Texas and its people. 
A valuable collection of material, anecdotical and statistical, which is not to be found 
in any other form. The work is handsomely illustrated. 



DICTIONARIES AND ENCYCLOPEDIAS. 
Home Cyclopaedia of Literature and Fine Arts. 

Index to terms employed hi belles-lettres, philosophy, theology, law, mythology, 
painting, music, sculpture, architecture, and all kindred arts. By Geo. Ripley and 
Chas. A. Dana. 

The Rhyming Dictionary. Walker. 

A serviceable manual to composers, being a complete index of allowable rhymes. 

Dictionary of Synonymes; or, The Topical Lexicon. 
Williams. 

Terms of the English language classified by subjects and arranged according to their 
affinities of meaning, with etymologies, definitions, and illustrations. A very enter- 
taining and instructive work. 

Hawaiian Dictionary. 

Mathematical Dictionary. Davies and Peck. 

A thorough compendium of the science, with illustrations and definitions. 

Kwong's Dictionary. 

A dictionary of English phrases. With illustrative sentences. With collections of 
English and Chinese proverbs, translations of Latin and French phrases, historical 
sketch of the Chinese^ Empire, a chronological list of the Chinese dynasties, brief 
biographical sketches of Confucius and of Jesus, and complete index. By Kwong Ki 
Chiu, late member of the Chinese Educational Mission in the United States, and for- 
merly principal teacher of English in the Government School at Shanghai, China. 900 
pages, 8vo, cloth. 



From the Hartford Courant. 
" The volume shows great industry and 
apprehension of our language, and is one 
of the most curious and interesting of 
linguistic works." 



From the New York Nation. 
" It will amaze the sand-lot gentry to be 
informed that this remarkable work will 
supplement our English dictionaries even 
for native Americans." 



BARNES'S LIBRARY OF BIOGRAPHY. 
The Life of President Garfield, 

From Birth to Presidency, by. Major J. M. Bundy, editor New York "Evening Mail- 
Express." From Mentor to Elberon, by Col. A. F. Rockwell. Oration and Eulogy, by 
Hon. James G. Blaine. 
This life of our martyred President, by Major Bundy, Mr. Blaine, and Colonel Rockwell, 

61 



THE NATIONAL SERIES OF STANDARD MISCELLANY. 

MISCELLANEOUS PUBLICATIONS — Continued. 

who was with the President before and after the assassination, is the most correct and 
authentic. Major Bundy visited General Gariield at Mentor, by invitation, and received 
all the facts relating to his life to the day of his nomination, from the General's lips. 
General Garfield showed his appreciation of it by recommending it to the Bepublican 
Committee as the book lie wished them to circulate. They showed their appreciation 
by circulating many thousands of copies among their speakers and friends. The por- 
trait was made under General and Mrs. Garfield's supervision, and gives altogether the 
best idea of the man, his face, head, and figure. The history of his life was completed 
by Colonel Rockwell. 

The Autobiography of Rev. Chas. G. Finney, 

The revivalist preacher and first president of Oberlin College. With steel portrait. 
Edited by Pres. J. H. Fairchild, of Oberlin. One vol., 12mo, cloth. Dr. Finney 
was the greatest and most successful evangelist of modern times. His labors extended 
not only throughout a large territory in the United States, but in Great Britain and 
Ireland, and he produced a most powerful impression. This memoir describes the 
scenes he passed through in the most vivid language, and covers the entire period of 
his life, from the time of his conversion to the close of his career. 

Memoirs of P. P. Bliss. 

With steel portrait of Mr. and Mrs. Bliss and two children. By Major D. W. Whittle. 
With a complete collection of Mr. Bliss's tunes and hymns, many of which are here 
published for the first time. Containing also contributions by Mr. Moody, Mr. Sankey, 
Dr. Goodwin, and others. 8vo, cloth, $2.00 ; cloth, gilt edges, $2.50. 

Every one knows the hymns, work, and tragic death of Mr. Bliss. This book should 
be on the shelves in every Christian household. 

The Life and Speeches of Henry Clay. 

New edition. Complete in one volume. Compiled and edited by Daniel Mallory. 
1,325 pages, 8vo, cloth, steel plates, portraits, and other illustrations. 

This is the best life of Henry Clay. It contains a full sketch of his life and all his 
speeches, — his most important speeches in full and his less important ones in part. It 
also contains an epitome of the Compromise Measures, the Obituary Addresses and 
Eulogies by Senators Underwood, Cass, Hunter, Hall, Clemens, Cooper, Jones, of Iowa, 
and Brooke; and Representatives Breckinridge, Ewing, Caskie, Chandler, of Pennsyl- 
vania, Bayley, Venable, Haven, Brooks, of New York, Faulkner, of Virginia, Parker, 
Gentry, Bowie, and Walsh. Also the funeral sermon, by the Rev. C. M Butler, Chap- 
lain of the Senate, and various important correspondence not elsewhere published. 

Henry Clay's Last Years. Colton. 
Garibaldi's Autobiography. 

From his birth to his retirement at Caprera ; including the most eventful period of 
his life. Translated from manuscript by Theodore Dwight, author of "A Tour in 
Italy," and " The Roman Republic." Embellished with portrait engraved on steel. 
12mo. 400 pages. 

The Life and Services of Lieut. -Gen. Winfield Scott, 

Including his brilliant achievements in the War of 1812 and in the Mexican War, and 
the part played by him at the opening of the Civil War of 1862. By Edward D. Mans- 
field, LL.D. 12mo, cloth, illustrated. 550 pages. 

Lives of the Signers. Dwight. 

The memory of the noble men who declared our country free, at the peril of their own 
" lives, fortunes, and sacred honor," should be embalmed in every American's heart. 

Life of Sir Joshua Reynolds. Cunningham. 

A candid, truthful, and appreciative memoir of the great painter, with a compilation 
of his discourses. The volume is a text-book for artists, as well as those who would 
acquire the rudiments of art. With a portrait. 

62 



f THE NATIONAL SERIES Of STANDARD MISCELLANY. 

MISCELLANEOUS PUBLICATIONS — Continued. 

Prison Life. 

Interesting biographies of celebrated prisoners and martyrs, designed especially for 
the instruction and cultivation of youth. 

Men of Mark. 

Bryant, Longfellow, Poe, Charles Tennyson Turner, Macaulay, Freeman, Curtius, 
George Tickuor, Sumner, John Stuart Mill. By Edwin P. Whipple, Edward A. Freeman, 
and others. 275 pages, 8vo, paper covers. 

The Hero of Cowpens. 

This book presents a complete history of the lives of heroic Daniel Morgan and of 
Benedict Arnold. These Revolutionary characters are viewed in varied lights, and the 
author has produced a most captivating historical sketch, as interesting as a romance. 

Autobiography of Havilah Mowry, Jr. 

A City missionary. 



BARNES'S LIBRARY OF TRAVEL. 
Silliman's Gallop among American Scenery; 

Or, Sketches of American Scenes and Military Adventure. By Augustus E. Silliman. 
338 pages, 8vo, illustrated. 

It is a mo.,t agreeable volume, and we commend it to the lovers of the " sparkling " 
style of literature. It carries the reader through and past many of the spots, North 
and South, made memorable by events of the Revolution and the War of 1S12. 

Texas : the Coming Empire. McDaniel and Taylor. 

Narrative of a two-thousand-mile trip on horseback through the Lone Star State; 
with lively descriptions of people, scenery, and resources. 

Life in the Sandwich Islands. Cheever. 

The " heart of the Pacific, as it was and is," shows most vividly the contrast between 
the depth of degradation and barbarism and the light and liberty of civilization, so 
rapidly realized in these islands under the humanizing influence of the Christian 
religion. Illustrated. 

The Republic of Liberia. Stockwell. 

This volume treats of the geography, climate, soil, and productions of this interesting 
country on the coast of Africa, with a history of its early settlement. Our colored 
citizens especially, from whom the founders of the new State went forth, should read 
Mr. StockwelPs account of it. It is so arranged as to be available for a school reader, 
and in colored schools is peculiarly appropriate as an instrument of education for the 
young. Liberia is likely to bear an important part in the future of their race. 

Discoveries among the Ruins of Nineveh and 
Babylon. 

With 20 illustrations and a complete index. By Austen H. Layard, M. P. Abridged 
edition. 550 pages, 12mo, cloth. 

Monasteries of the East. 

Embracing descriptions from personal observation of Egypt in 1833 ; the Natron 
Lakes, the Convent of the Pulley, the Ruined Monastery at Thebes, the White Monas- 
tery, the Island of Philoe, &c, Jerusalem, the Monastery of St. Sabba, and the Mon- 
asteries of Metesra, Saint Athos. By Robert Curzon, Jr. 400 pages, 12mo, cloth. 

A Run through Europe. 

By Hon. Erastus C. Benedict, late Chancellor of the University of New York. A six 
months' tour through the galleries and capitals of Europe, by a most intelligent observer, 
in the year 1867. 12mo, cloth. 

63 



THE NATIONAL SERIES OF STANDARD MISCELLANY. 

MISCELLANEOUS PUBLICATIONS - Continued. 

Eighteen Months on a Greenland Whaler. 

By Joseph P. Faulkner, an "ex-assistant whale-catcher in an American schooner," and 
author of other recollections of the sea. 318 pages, i6mo, cloth. 



The Polar Regions ; 

Or, The First Search After Sir John Franklin's Expedition. By Lieut. Sherard Osborn, 
commanding H. M. S. Pioneer (the first steam vessel that ever penetrated the Northern 
sea). 212 pages, 12mo, cloth. 

St. Petersburg. Jermann. 

Americans are less familiar with the history and social customs of the Russian peo- 
ple than those of any other modern civilized nation. Opportunities such as this book 
affords are not, therefore, to be neglected. 

Thirteen Months in the Confederate Army. 

The author, a Northern man conscripted into the Confederate service, and rising from 
the ranks by soldierly conduct to positions of responsibility, had remarkable oppor- 
tunities for the acquisition of facts respecting the conduct of the Southern armies, and 
the policy and deeds of their leaders. He participated in many engagements, and his 
book is one of the most exciting narratives of adventure ever published. Mr. Steven- 
son takes no ground as a partisan, but views the whole subject as with the eye of a 
neutral, only interested in subserving the ends of history by the contribution of 
impartial facts. Illustrated. 

The Isthmus of Tehauntepec. Anderson. 

8vo, cloth. A history of the Isthmus from earliest times to the present, wYh an 
account of -ailroad enterprises and valuable maps and charts. 



BARNES'S RELIGIOUS LIBRARY. 
Ray Palmer's Poetical Works. 

An exquisite edition of the complete hymns and other poetical writings of the 
most eminent of American sacred poets, author of " My Faith Looks up to Thee." 

Formation of Religious Opinions. Palmer. 

Hints for the benefit of young people who have found themselves disturbed by inward 
questionings or doubts concerning the Christian faith. 

Nine Lectures on Preaching. Dale. 

By Rev. R. W. Dale, of England. Delivered at Yale, College. Contents : Perils of Young 
Preachers ; The Intellect in Relation to Preaching ; Reading ; Preparation of Sermons ; 
Extemporaneous Preaching ; Evangelistic Preaching ; Pastoral Preaching ; Conduct 
of Public Worship. 

Dale on the Atonement. 

The theory and fact of Christ's atonement profoundly considered. 

The Service of Song. Stacy. 

A treatise on singing, in public and private devotion. Its history, office, and impor- 
tance considered. 

" Remember Me." Palmer. 

Preparation for the Holy Communion. 

Bible Lands Illustrated. 

A pictorial hand-book of the antiquities and modern life of all the sacred countries. 
By Henry C. Fish, D.D. With six hundred engravings and maps, one thousand eluci- 
dated Scripture texts, and two thousand indexed subjects. 8vo, cloth, 900 

64 



THE NATIONAL SERIES OF STANDARD MISCELLANY. 



MISCELLANEOUS PUBLICATIONS — Continued. 

Lyman Abbott's Commentary on the Gospels. 

Handy edition, 3 vols., Svo, 
cloth, illustrated. Household 
edition, on large paper, in 2 
vols. 

This is altogether, and all 
points considered, the best 
commentary for Christian 
workers. It is handy, prac- 
tical, finely illustrated and 
printed, clear, concise, plain, 
spiritual, and scholarly. It 
is cordially and earnestly 
indorsed by the most emi- 
nent divines and laymen of 
all denominations, and also 
by the whole religious press. 

" Ellicott and Alvord are 
too costly and too learned; 
Barnes, Jacobus, and Owen 
are too flat and thin ; Lange 
is a huge wilderness ; Abbott 
is simple, attractive, correct, 
and judicious in the use 
of learning." — Chancellor 
Howard Crosby, LL D. 

" We are strongly con- 
vinced that this is one of the 
ablest commentaries which 
this century of commenta- 
ries has produced." — Rev. 
J. H. Vincent, D.D. 




Eastern City Wall. [From Abbott's Commentary.! 



Lady Willoughby. 



The diary of a wile and mother. An historical romance of the seventeenth century. 
At once beautiful and pathetic, entertaining and instructive. 

Favorite Hymns Restored. Gage. 

Most of the standard hymns have undergone modification or abridgment by compilers, 
but this volume contains them exactly as written by the authors. 

Poets' Gift of Consolation. 

A beautiful selection of poems referring to the death of children. 

The Mosaic Account of Creation. 

The Miracle of To-Day ; or, New Witnesses of the Oneness of Genesis and Science. 
With essays on the cause and epoch of the present inclination of the earth's axis, and 
on Cosmology. By Charles B. Warring. 



65 



THE NATIONAL SERIES Of STANDARD MISCELLANY. 

MISCELLANEOUS PUBLICATIONS — Continued, 

Froude's Theological Unrest. (Atlas Series.) 
The History of the English Bible, 

Extending from the earliest Saxon translations to the present Anglo-American Revision. 
With special reference to the Protestant religion and the English language. By Black- 
ford Condit. With steel portrait of Wycliffe. 400 pages. 12mo, cloth. 

This is a consecutive history of all the English versions of the Scriptures and their 
translators, including also the history of Protestantism in England and the growth and 
changes of the English language. 



BARNES'S YOUTH'S LIBRARY. 

c 

Earnest Words on True Success in Life. 

Addressed to young men and women. By Ray Palmer. 296 pages, 12mo, clotn. 

Ida Norman. 

Two vols, in one. A novel. With illustrations. By Mrs. Lincoln Phelps. 432 pages, 
12mo, cloth. 

The Educator ; or, Hours with my Pupils. 

A series of practical hints to young ladies on questions of behavior and education. 
By Mrs. Lincoln Phelps. 364 pages, 12mo, cloth. 

The Student ; or, the Fireside Friend. 

A series of lectures to young ladies, in which the author gives a course of practical 
instruction for home study, including physical, intellectual, social, domestic, and relig- 
ious training. Intended to awaken in the minds of the young an idea of the impor- 
tance and value of education, and to provide the means of self-instruction. With an 
index. 380 pages, 12mo, cloth. 

Monasteries of the East. 

Embracing visits to monasteries in the Levant. By the Hon. Robert Curzon, Jr. 
416 pages, 12mo, cloth. 

Life in the Sandwich Islands. 

By Rev. Henry T. Cheever. 356 pages, 12mo, cloth. 

Lives of the Signers. 

Carefully prepared sketches of the lives and careers of the signers of the document 
declaring the independence of the States of America. By N. Dwight. 374 pages, 12mo, 
cloth. 

Discoveries among the Ruins of Nineveh and 
Babylon. 

With travels in Armenia, Kurdistan, and the Desert. Being the result of the second 
expedition undertaken for the trustees of the British Museum. An abridgment. By 
Austen H. Layard, M.P. 550 pages, 12mo, cloth. 

The History of the Jews. 

From the flood to their dispersement. From sources sacred and profane. A most 
excellent work in connection with the study of the Scriptures. Giving a connected 
account of the history and acts of this chosen people. By Abraham Mills, with colored 
charts, maps, and illustrations. 444 pages, 12mo. 

Johnny Morrow, the Newsboy. 

An autobiography written by the hero when sixteen years of age. 16mo, cloth. A 
plain story of one who represents a class. The writer, although a newsboy and pedler 
of trinkets, is well remembered in New Haven, Conn., and possesses a power and 
maturity of expression quite remarkable. 

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